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The non-polynomial THINC (tangent of hyperbola for interface capturing) scheme has been reported to show both numerical simplicity and high fidelity for resolving contact interfaces. In this paper, two types of smooth sigmoid functions are employed to construct the non-polynomial reconstructions for capturing interfaces (similarly, called SFINC schemes, sigmoid functions for interface capturing). One type is that the exact jump location (a parameter introduced in the reconstruction) can be analytically calculated, and another type cannot. The algebraic function and the Gudermannian function belong to the first and the second types, respectively, and are investigated in this paper. An approximate method for calculating the jump location of the Gudermannian function is proposed. The method avoids the iteration process of determining the jump location, and hence is efficient and practical in applications. The numerical validations and comparisons of SFINC schemes are presented to show their performance for simulating complex compressible flow fields. • The interface capturing schemes based on the sigmoid functions are developed. • The approximate methods are proposed to determine the jump location of the Gudermannian method. • A workable range of the steepness parameter in capturing interfaces is evaluated. • Numerical examples are presented to validate and compare the proposed schemes. [ABSTRACT FROM AUTHOR]

This paper focuses on the design and analysis of very high-order finite volume methods for the computation of simplified meso- and micro-scale atmospheric flows. In a dry atmosphere, these flows can be represented by the Euler equations with a gravitational source term. Two different approaches are considered here. While one of the approaches is fully conservative for the total energy, the other is formulated in a non-conservative form. The main focus of the paper is to analyze the performance of such models in combination with the traditional WENO reconstruction and the novel TENO reconstruction by examining the spectral properties of these reconstruction methods. The overarching goal is to determine whether the combination of these models and numerical schemes can be used to build an implicit Large Eddy Simulation framework, shedding light on their potential advantages or limitations in representing under-resolved atmospheric processes in the meso- and micro-scales. • Finite volume schemes based on WENO and TENO reconstructions are assessed. • WENO and TENO reconstructions allow to develop an iLES solver for atmospheric flows. • The inertial sub-range of under-resolved atmospheric turbulent flows is well captured. [ABSTRACT FROM AUTHOR]

• Lagrange's equation for fluid mechanics is proposed with power functional. • Fluid part of VFIFE method is explored via fractional steps. • A MATLAB program based on VFIFE-LES turbulence model is developed. • Theoretical basis for the unified fluid-solid dynamics in VFIFE is provided. • The method is effective in improving the convergence and numerical oscillation. Vector form of intrinsic finite element (VFIFE) is a numerical method widely used in solid mechanics. However, it's hard to extend the VFIFE method to fluid mechanics since the traditional VFIFE method fails to reflect the analytical equilibrium of multiple variables in the continuum. Therefore, under the framework of analytical mechanics, this paper proposes Lagrange's equation of the second kind in fluid mechanics with the extremum condition of Lagrange power functional. And a vectorized motion equation of incompressible viscous fluids is deduced from Lagrange's equation. By using several efficient algorithms in the finite difference method (FDM) and the finite element method (FEM), the NS equation is decomposed into four governing equations of vector form for fluid mechanics. In addition, with the application of the classic Smagorinsky sub-grid scale model in large eddy simulation (LES), this paper puts forward turbulence modelling with VFIFE procedure, and a corresponding MATLAB program is developed. Two typical examples are given to demonstrate the applicability and efficiency of the proposed large eddy simulation with VFIFE method. The proposed algorithm can effectively eliminate the non-physical oscillation of the pressure, and obtain much accurate results with a small number of grids. [ABSTRACT FROM AUTHOR]

• Develop a consistent second order ISPH model (ISPH_CQ) for solving the free surface problems, in which all the Laplacian and gradient operations are directly discretised by the quadric semi-analytical finite difference interpolation scheme (QSFDI). • This is the first ISPH model demonstrating a second order convergence for solving the pressure Poisson's equation in a blended form consisting of both the velocity divergence and density variation term. • Carry out a systematic comparative study on the accuracy, convergence, robustness, mass/energy conservation and the capacity on reproducing the pressure field using various cases with free surface flows, including oscillating liquid drop, wave propagations and liquid sloshing. The Incompressible Smoothed Particle Hydrodynamics (ISPH) is now a popular numerical method for modelling free surface flows, in particular the breaking waves and violent wave-structures interaction. The ISPH requires the projection approach, leading to solving a pressure Poisson's equation (PPE). Although the accuracy and convergence of the numerical scheme to discretise the Laplacian operator involved in PPE is critical for securing a satisfactory solution of the PPE, the overall performance of the ISPH is also influenced by other key numerical implementations, including (1) estimation of the viscous terms; (2) calculation of the velocity divergence; (3) discretisation of the boundary conditions for the PPE; and (4) evaluation of the pressure gradient. In our previous paper [29] , the quadratic semi-analytical finite difference interpolation scheme (QSFDI), which has a leading truncation error at third order derivatives, has been adopted to discretise the Laplacian operator. In this paper, the QSFDI will be adopted, not only for discretising the Laplacian operator, but also for approximating viscous terms, velocity divergence, boundary conditions and pressure gradient. The performance of the newly formulated consistent second order ISPH is assessed by various cases including the oscillating liquid drop, the wave propagation, and the liquid sloshing. The results do not only demonstrate a second order convergence over a limited range of conditions and a higher computational efficiency, i.e., requiring less computational time to achieve the same accuracy, but also show a better mass/energy conservation property and capacity of reproducing a smooth pressure field, than other ISPH models considered in this study. [ABSTRACT FROM AUTHOR]

• This article is focused on the numerical study of relative two-particle diffusion in homogeneous turbulence with stable stratification. • We developed a simplified model to facilitate the analysis and use the Lagrangian two-time velocity correlation to obtain components of tensors associated with one-particle and two-particle diffusion. • The paper highlights the t3 law for horizontal diffusion conditions and provides a direct estimate of the validity interval of this law. • Additionally, the authors apply the same procedure to highlight the 4/3 diffusivity law. • Overall, this present article provides valuable insights into the behavior of two-particle diffusion in homogeneous turbulence with stable stratification. This paper investigates the numerical study of relative two-particle diffusion in homogeneous stably stratified turbulence. The focus is on obtaining components of tensors Δ (t ′ , t) and Δ r (t) which are associated with one-particle and two-particle diffusion, respectively. This is achieved by utilizing Lagrangian two-time velocity correlations for both individual particles and two particles initially separated by δ x 0 →. To facilitate the analysis, a simple two-particle diffusion model is developed based on assumptions similar to previous works by Kaneda and Ishida, as well as Ishihara and Kaneda, to elaborate one-particle and two-particle diffusion models. Using this model, Lagrangian two-time velocity correlations are calculated from numerically obtained two-time correlations spectra using a linear analysis RDT (rapid distortion theory) or the so-called rapid distortion approximation in the spectral space. The components of the two-particle diffusion tensor are then deduced directly. This study employs linear solutions of the Navier-Stokes equations using the Boussinesq approximation to describe stably stratified turbulence. The application of this two-particle diffusion model considers an initial turbulence with a Reynolds number R λ = 2022.80 associated with the Taylor micro-scale of 2022.80. In this article, a large Reynolds number (R L = 270,957) was chosen to study the characteristics of homogeneous stably stratified turbulence. The choice of a large Reynolds number allows for the investigation of turbulence at smaller scales and provides a more detailed understanding of the flow dynamics. Two values of the Froude number (Fr) are selected: Fr=0.0026 and Fr=0.0045, in accordance with previously adopted criteria. Additionally, different values of the vertical displacement δ x 0 / η are chosen, where (η) represents the Kolmogorov length-scale. Ultimately, two numerical simulation series are conducted: R λ =2022.80, Fr=0.0045, δ x 0 / η =15, 17, 20, 24 and R λ =2022.80, Fr=0.0026, δ x 0 / η =15, 20, 25. The primary objective of this study is to delve into the fundamental problem of highlighting the t 3 Richardson law and the 4/3 diffusivity Richardson law in the horizontal plane during the intermediate range of times, focusing on two-particle diffusion. [ABSTRACT FROM AUTHOR]

Artificial upwelling by the use of airlift pump is regarded as an effective way in utilizing deep ocean water and actualizing ocean fertilization. This paper focuses on numerical analysis of steady air–water two-phase flow in a vertical pipe of an airlift system based on one-dimensional multi-fluid model. The depth distributions of 6 physical quantities such as volumetric fractions and axial velocities of two phases, air density and pressure are calculated by solving the governing equations or by integrating the vector form of nonhomogeneous ordinary differential equation for two-phase flow interval. Upon successful verification of the present numerical model through a comparison with precedent theoretical and experimental results in case of a vertical pipe with length of 7.86 m, the model is extended to the case of artificial upwelling from water depth of 2000 m. The effects of submerged depth of air–water mixer on the pumped amount of water and the depth distributions of 6 physical quantities are considered. • This paper is concerned with numerical analysis of steady air–water two-phase flow in a vertical pipe of an airlift system to lift deep ocean water. • The depth distributions of 6 physical quantities such as volumetric fractions and axial velocities of two phases, air density and pressure are obtained from one-dimensional multi-fluid model. • The present model can be applied to predict the performance of airlift pump for lifting deep ocean water and the depth distributions of 6 physical quantities in axial direction. [ABSTRACT FROM AUTHOR]

• A coupling method of the smoothed particle hydrodynamics (SPH) method and the finite volume method (FVM) is optimized in this paper. • Validation of the deformation behaviour of droplets in oil using a coupled SPH-FVM approach. • The effects of capillary number, electrical conductivity and dielectric ratio on droplet deformation are investigated based on an optimized coupled FVM and SPH method in this paper. In the numerical simulation of droplet electrohydrodynamic deformation, the grid-based method is difficult to handle the large topological deformation of the droplet interface, while the meshless method is challenging in the enforcement of boundary conditions. Therefore, a coupling method of the smoothed particle hydrodynamics (SPH) method and the finite volume method (FVM) is developed in this paper. In the present coupling method, the SPH method is used to solve the governing equations of the two-phase flow, while the FVM is used to solve the governing equations of the electric field. The realization of the coupling method is based on the information transfer between particles and grids. In order to accurately transfer the electric field force of interface grid nodes to SPH particles, a particle splitting interpolation method is developed. The influences of electrical capillary number, electrical conductivity ratio, and permittivity ratio on droplet deformation are studied. The simulation results are in good agreement with the theoretical predictions, and the coupling method can obtain more accurate numerical results than the pure SPH method. The coupling method can provide a reliable way to investigate complex electrohydrodynamic problems. [ABSTRACT FROM AUTHOR]

The bilayer shallow water wave equations in one-dimensional space are considered in this paper. The equations admit two groups of characteristic velocities, which are the first-order approximation of the eigenvalues. Due to the numerical instability, the characteristic velocities may become complex, and thus the system is not hyperbolic and yields to the so-called Kelvin–Helmholtz instability at the interface of the two layers. To overcome this issue, an invariant domain preserving DG method is presented for the bilayer shallow water wave equations. The proposed method is high-order accurate, conservative and can keep the characteristic velocities being real provided that the initial characteristic velocities are real. Therefore, the Kelvin–Helmholtz instability at the interface can be avoided. Representative numerical examples are chose to demonstrate the performance of the proposed method. • The bilayer shallow water wave equations are considered in this paper. • A high-order domain preserving DG method is presented in this paper. • The Kelvin–Helmholtz instability at the interface is removed. [ABSTRACT FROM AUTHOR]

In recent decades, the arbitrary Lagrangian–Eulerian (ALE) approach has been one of the most popular choices to deal with the fluid flows having moving boundaries. The ALE finite volume (FV) method is well-known for its capability of shock capturing. Several ALE discontinuous Galerkin (DG) methods are developed to fully explore the advantages of high-order methods, especially in complex flows. The DG scheme is highly efficient and has high resolution in smooth parts of the flow while the FV scheme has advantage on the robustness against shocks. In this paper, we present a novel algorithm to combine both the ALE FV and ALE DG methods into one stable and efficient hybrid approach. The main challenge for a mixed ALE FV method and ALE DG method is to reduce the inconsistency between both discretizations. Of particular concern are the same mesh velocity distribution between DG and FV elements and a continuous mesh velocity at the coupling interfaces. Since the computational efficiency of the proposed algorithm is of major concern, performance aspects will be considered during the construction of the scheme. To investigate the accuracy of the new scheme, several benchmark test cases with prescribed movements are included. Afterwards, the algorithm is applied to more general and complex scenarios to show its ability to cope with complex setups. In our paper, the scheme is implemented into a loosely-coupled fluid–structure interaction (FSI) framework. With a shock-driven cylinder movement in a channel flow and a transonic flow-induced airfoil vibration, we demonstrate our method for FSI applications. • A new algorithm for shock capturing in high-order arbitrary Lagrangian-Eulerian discontinuous Galerkin spectral element method background. • The inconsistency due to the employment of a mixed DG/FV scheme is reduced to meet the requirement of the geometric conservation law in a moving mesh scenario. • The new algorithm is applied to fluid flows with prescribed mesh movement, and more general fluid–structure interaction induced moving mesh problems. [ABSTRACT FROM AUTHOR]

The paper describes the implementation of thermodynamic modelling within a high-order finite difference scheme. A new method to ensure thermodynamic consistency for Navier–Stokes simulations of real-gas 1 1 A real gas being one which does not obey the ideal gas law. flows is outlined. The paper shows that this method is suited to high fidelity simulations of dense-vapour flows with complex equations of state, such as found in Organic Rankine Cycle turbines. The method is illustrated with two examples of siloxane MM flow in a channel and in a turbine vane. The results show that thermodynamic consistency plays a vital role in the accurate prediction of irreversibility and therefore turbine loss. • A new method for consistent thermodynamic modelling is proposed • The method is suited to Navier-Stokes simulations of real gas and dense vapour flows • The method avoids the high computational cost of Helmholtz equations of state • The method retains high accuracy and thermodynamic consistency [ABSTRACT FROM AUTHOR]

The growing availability of large scale computing power and facilities has caused a potential for increased accuracy in CFD simulations, allowing scientists and engineers to look beyond traditional Reynolds-Averaged Navier–Stokes (RANS approaches) in favor of high-fidelity simulations, characterized by high resolution in space and time, for industrially relevant flow configurations. In situ analysis and visualization is a promising solution in the exascale supercomputing era to reduce the size of data stored on disk and time spent for post-processing by using all available resources. This paper quantifies the impact of a tightly-coupled in situ approach based on ParaView Catalyst on three different codes, namely OpenFOAM, STREAmS, and MIGALE, which implement different numerical schemes and operate in different contexts (research field rather than industrial field). We show that the overhead is not negligible, it can be of the same order as the solution of the Navier–Stokes equations depending on the type of simulation, but in any case it does not prevent to solve the physical challenge under investigation. • The paper provides information about the actual implementation effort and computational cost of the approach to include in situ in a CFD code from scratch. • The paper quantifies the impact of a tightly-coupled in situ approach based on ParaView Catalyst on three different codes, namely OpenFOAM, STREAmS, and MIGALE, which they implement different numerical discretizations of the Navier–Stokes equations. • The overhead of in situ post-processing can be of the same order as the solution of the Navier–Stokes equations in high-fidelity simulations, characterized by high resolution in space and time. • The paper shows a limited impact of in situ visualization on the weak scalability of STREAmS in the range of 8-512 GPUs. [ABSTRACT FROM AUTHOR]

The current work presents an innovative numerical technique for high-Reynolds/high-Mach number compressible flow simulations in complex configurations. In particular, the research combines a novel wall-modeled large-eddy simulation technique with a sharp-interface immersed boundary method in the framework of high-order numerical schemes. The proposed approach enables the best from wall modeling and the immersed boundary. The first is concerned with accurately dealing with wall flows while avoiding direct control of near-wall resolution; the second is related to efficiently treating arbitrarily complex geometries in Cartesian grids. In particular, the paper extends a well-established wall model already presented by the research group to arbitrarily-shaped bounds. The method yields a minimally invasive technique that switches between wall-resolved and wall-modeled large-eddy simulations according to the local near-wall resolution. Thus, easily fitting aerodynamic simulation needs. After discussing the numerical procedure, the paper provides several benchmarks to demonstrate the validity of the proposed approach. In particular, literature-available direct numerical datasets are mined to compare acquired outcomes. The results' accuracy is found to be remarkable from low-Mach-channel and -pipe flow configurations up highly-compressible flows concerning the spatial deployment of the boundary layer over a flat plate and the shock-wave/boundary-layer interaction over a compression ramp. Thus, the proposed method appears to be a promising framework for dealing with engineering-relevant flow simulations along with the efficient path of Cartesian meshes combined with massively parallel GPU-accelerated architectures. [ABSTRACT FROM AUTHOR]

We are developing a new technique for monitoring portal hypertension by the pressure gradient between the portal vein and the inferior vena cava (PPG) based on non-invasive measurements (MRI images). Massive parametrization and classification are required to investigate the underlying relationship between the porosity and the stages of liver cirrhosis numerically, and the hepatic-portal venous system is a multi-scale system. Both of them need high computational costs. The suitability of the lattice Boltzmann method for GPU (Graphics Processing Unit) parallel computation provides an opportunity to overcome it. In this paper, we perform GPU parallelization and optimization for the volumetric lattice Boltzmann method with arbitrary geometry based on images. Three application cases, including pipe flow, hemodynamics in the portal venous system, and hemodynamics in a simple hepatic-portal venous system, are employed to prove the method can be applied in the hepatic-portal venous system based on accuracy and efficiency. The reliability of the model is qualitatively validated by the analytical solution of velocity and pressure difference distribution of pipe flow and quantitatively confirmed by the pulsatility of velocity and pressure difference that can be neglected in the portal venous system. The performance of the application cases is examined with Intel Broadwell E5-2683 v3@ 2.30 GHz (CPU) and NVIDIA Tesla V100 16GB (GPU). It shows the GPU algorithm for sparse geometry (SPARSE) has a similar speed to the regular GPU algorithm for dense geometry (DENSE) when the fluid volume fraction (q) is close to 1. And SPARSE speeds up to 2.2 times compared with DENSE when q is in the range of 0.19 ∼ 0.27. Meanwhile, the saving ratio of memory cost depends on q. For a numerical case in the hepatic-portal venous system, i.e., a large-scale system, parallel execution can be converged around half an hour with SPARSE, while the memory spills the limitation with DENSE with a single GPU. Hence, multi-GPU implementation is applied to release the limitation, and it can improve performance by increasing the number of GPU cards. In summary, the method presented in the paper is feasibility applied in the hepatic-portal venous system, laying the foundation of the new technique development. • GPU accelerated volumetric lattice Boltzmann model to investigate a new technique to monitor portal hypertension in the hepatic-portal venous system is feasible. • GPU algorithm for sparse geometry (SPARSE) has a similar speed to the regular GPU algorithm for dense geometry (DENSE) when the fluid volume fraction (q) is close to 1. And SPARSE speeds up to 2.2 times compared with DENSE when q is in the range of 0.19 ∼ 0.27. • Multi-GPU implementation is applied to release the limitation, and it can improve performance by increasing the number of GPU cards. [ABSTRACT FROM AUTHOR]

• A three-dimensional (3D) high-order flux reconstruction lattice boltzmann flux solver (FR-LBFS) is developed in this paper for the accurate and efficient simulation of incompressible laminar and turbulent flows. • The FR-LBFS inherits the superiority of LBFS and FR and shares the following attractive features: (i) a fully-explicit arbitrary order compact method, (ii) weakly compressible (WC) model for unsteady incompressible flows and (iii) evaluating inviscid and viscous fluxes simultaneously. • The proposed solver has better stability compared with FR based compressible Navier-Stokes solver when simulating incompressible decaying homogeneous isotropic turbulent flow. • The present 3D FR-LBFS is a promising tool for under-resolved or implicit large eddy simulation (ILES) of incompressible homogeneous and wall bounded turbulent flows. A three-dimensional (3D) high-order flux reconstruction lattice Boltzmann flux solver (FR-LBFS) is developed in this paper for accurate and efficient simulations of incompressible laminar and turbulent flows. The original lattice Boltzmann flux solver (LBFS) is a second-order finite volume method (FVM) which combines the advantages of conventional Navier-Stokes (N-S) solvers and lattice Boltzmann equation (LBE) solvers. But it is not convenient to construct high-order FVM, and the compactness is always a bottleneck. The present work separates LBFS from FVM and combines LBFS with high-order FR scheme. Thus, the FR-LBFS inherits the superiority of LBFS and FR and shares the following attractive features: (i) a fully-explicit arbitrary order compact method, (ii) weakly compressible (WC) model for unsteady incompressible flows and (iii) evaluating inviscid and viscous fluxes simultaneously and no particular technique requirement, such as local discontinuous Galerkin method (LDG), for viscous term discretization. To validate the current method, various 3D incompressible laminar isothermal and thermal numerical experiments are presented first. Good agreements are achieved between the current results and the previous experimental and numerical data whilst the present high-order solver adopt coarse meshes. Furthermore, the ability of the proposed method to perform accurate and stable computations of incompressible decaying homogeneous isotropic turbulent flows and turbulent channel flows with different mesh resolutions and accuracy orders are investigated. The results show that the present 3D FR-LBFS is a promising tool for under-resolved or implicit large eddy simulation (ILES) of incompressible turbulent flows. [ABSTRACT FROM AUTHOR]

The paper describes the development of a Cartesian method able of simulating compressible and viscous flows around moving/deforming objects as well as fluid–structure interactions (FSI). Besides, the research addresses the issues related to the partitioned coupling of aerodynamic and structural tools and suggests the use of proper drivers based on open-source libraries. The flow solver is based on dynamic immersed boundaries (IB) which take into account the motion of Lagrangian bodies through an inertial Cartesian mesh. This means having cells without volume changes and/or roto-translations. In particular, the major difficulties arise from the correct evaluation of flow quantities at cells emerging from the solid areas. Indeed, no flow-state is associated with cells inside the body. As a consequence, a 'field-extension' procedure is applied to estimate the flow state vector where needed. The use of fluid and wall values makes the procedure consistent. A proper IB model accounts for the body motion into a stationary mesh that are dynamically adapted to the flow. Both rigid and deforming motions are allowed by means of proper BCs based on the local wall-velocities. The paper discusses the accuracy and stability constraints of the method when applied to well-known benchmarks available in literature. In particular, the ability to analyze rigid body-motions is assessed by simulating the viscous flows around an oscillating circular cylinder and a moving sphere. Both cases focus on the laminar regime which represents an effective starting-point for validating the dynamic IB-method. Part of the research activities is devoted to developing an interface for coupling the present method with a structural solver in the framework of a partitioned process. A shared platform is set-up for driving the solution sequence and analyzing the accuracy of the results. A literature case is discussed which consists of a flexible cantilever mounted in the laminar wake of a rigid square cylinder. The final aim is to make affordable the study of complex flows whose characteristics strongly depend on the structural dynamics of immersed objects. In particular, the use of an IB method based on a fast and automatic meshing process is expected to simplify and speed-up the simulation of fluid–structure interaction (FSI) problems. • A Cartesian method able of simulating viscous flows around moving/deforming objects • "Dynamic" immersed boundaries (IB) through an inertial Cartesian mesh. • Numerical analyses in overall agreement with the literature data. [ABSTRACT FROM AUTHOR]

The potential of sequential Data Assimilation (DA) techniques to improve the numerical accuracy of Large Eddy Simulation (LES) performed on coarse grid is assessed. Specifically, this paper evaluates the performance of the Multigrid Ensemble Kalman Filter (MGEnKF) method, recently introduced by Moldovan, Lehnasch, Cordier and Meldi (Journal of Computational Physics, 2021). The international benchmark referred to as BARC (Benchmark of the Aerodynamics of a Rectangular 5:1 Cylinder) is chosen as test configuration, as it includes several complex flow dynamics encountered in turbulence studies. The results for the statistical moments of the velocity and pressure flow field show that the data-driven techniques employed are able to significantly improve the predictive features of the solver for reduced grid resolution. In addition, it was observed that, despite the sparse and asymmetric distribution of observation in the data-driven process, the DA augmented LES exhibits symmetric statistics and a significantly improved accuracy also far from the observation zone. • The MGEnKF is used to augment LES in the high-Reynolds-number in the BARC test case. • The filtering is sequentially performed using instantaneous flow information. • Observation is assimilated on-the-fly. • Results show that the MGEnKF improves the predictive capabilities of the LES model. [ABSTRACT FROM AUTHOR]

• Implicit algorithms is established based on Boltzmann model equation. • The DRIA gas surface interaction model is incorporated in the implicit algorithms. • The effects of energy accommodation at various surface thermal states on flow fields are explored. To study the influence of energy accommodation of scattering gas molecules on flow fields during large expired spacecraft reentry, a more elaborated gas-surface interaction model, compared with full Maxwellian diffuse model, is employed in implicit algorithms based on Boltzmann model equation. The characteristic distributions around cylinder at different fluid regimes are accordingly obtained by implicit algorithms, Navier-Stokes solver and DSMC ((Direct Simulation Monte Carlo) method. And the consistency of these results is verified. It is confirmed that present algorithms are capable of solving external flow problems covering various fluid regimes. Then the simulation results see that under current conditions set in the paper, pressure and temperature are proportional to wall activation (ω = T w / T ∞ , T w is surface temperature, T ∞ denotes as free stream temperature), but their amplitudes alter with ω at different fluid regimes. As for the effects of energy accommodation coefficients (α e), both pressure and temperature profiles vary in a linear way with α e. However, the variation ranges of these parameters are diverse with regard to different fluid regimes. These observations are favor to the construction of efficient forecasting software, which could predict the flight path of large defunct spacecraft. In this forecasting software, the external ballistics computations and aerothermodynamic simulations are synchronously carried out. [ABSTRACT FROM AUTHOR]

Recently, Qi et al. (2022) and Guo et al. (2023) proposed two alternative designs of an efficient mesoscopic method using the total-energy double-distribution-function (DDF) formulation, hereafter referred to as the Qi model and the Guo model. The two models share the same advantage of using only 40 discrete particle velocities to fully reproduce the Navier–Stokes-Fourier (NSF) system. However, the Guo model is based on a more rigorous kinetic consideration, while the Qi model relies on a more general design of the source term to allow for adjustable bulk-to-shear viscosity ratio. In this paper, we derive lifting relations for the Qi model based on two alternative approaches, namely, the Hermite expansion and the Chapman–Enskog expansion, which can be used to construct the boundary and initial conditions for the mesoscopic method. For three-dimensional compressible turbulence simulations, including compressible decaying homogeneous isotropic turbulence and Taylor–Green vortex flows, the derived two sets of lifting relations are applied to the initialization distribution function to study their impacts. Interestingly, for the Qi model, the two sets of lifting relations yield the same results without numerical artifacts, whereas for the Guo model, an appropriate lifting relation must be specified to avoid numerical artifacts resulting from the flow initialization (Qi et al., 2023). • Lifting relations in the Qi model are derived by two alternative methods. • Our lifting relations can be applied to initialize the compressible flow simulations. • Two sets of lifting relations yield the same results without numerical artifacts. [ABSTRACT FROM AUTHOR]

The mass-, energy-, and potential-enstrophy-conserving Poisson bracket numerical scheme introduced by Arakawa & Lamb (1981), and extended by Salmon (2004) and Stewart & Dellar (2016), is adapted to the problem of nonlinear shallow-water sloshing over a variable bottom surface in a rigid rectangular basin undergoing a prescribed coupled surge-sway motion. Adaptation to a finite domain requires a new approach to the boundary conditions at solid boundaries in the context of the Arakawa C grid. In this paper, the boundary condition at the vertical walls is taken to be vanishing of the normal derivative of the tangential velocity. This gives zero potential vorticity at the boundary, and is consistent with the material conservation of the potential vorticity. This condition, coupled to symmetric boundary conditions for the wave height arising from a reduced version of the evolution equations at boundaries, leads to an extension of the class of staggered C-grid Poisson-bracket schemes to interior flows with solid boundaries. The scheme is implemented, shown to preserve Casimirs, and applied to a range of problems in shallow water hydrodynamics including interaction of travelling hydraulic jumps at resonance, and X-type soliton interactions over a variable bottom surface. This structure-preserving scheme provides a robust building block for long-time simulation of floating ocean wave energy extractors. • Developing a Poisson-bracket scheme for nonlinear shallow-water sloshing. • Presenting a new approach to the sloshing boundary conditions on the Arakawa C grid. • Presenting new long-time sloshing numerical simulations. • Discussion of generalised Poisson-bracket schemes for wave energy extraction. [ABSTRACT FROM AUTHOR]

There is a great influence of the melt filling process on the quality of castings. Smoothed particle hydrodynamics (SPH) that materials are approximated by free particles rather than by fixed grids is applied to accurately predict fluid flows involving complex free surfaces. In this paper we present a mathematical model of melt flow and heat transfer by using SPH method. A novel approach is used in the governing equations to ensure stable numerical schemes and homogeneous particle distributions. The SPH heat equation takes into account the thermal release during phase transition and is more suitable for alloy solidification. The solid wall boundary conditions are slightly modified to satisfy the filling simulations. Several case studies are carried out to predict significant details about the filling order and flow structures in the mold cavity. The velocity and temperature distributions during different stages of melt filling are also given. The results show that this proposed model allows us to understand the predisposition of defects such as gas porosity and weld lines in the castings. These predictions can be used as inputs for improving process parameters, venting and cooling systems design. • Particle transport velocity corrected by pressure is added in governing equations. • Normal direction of solid wall particle is introduced in boundary conditions. • Stable numerical schemes and homogeneous particle distributions. • SPH filling help understand defect formation and optimize process design. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned about the lattice Boltzmann methods (LBMs) based on vector-kinetic models for hyperbolic partial differential equations. In addition to usual lattice Boltzmann equation (LBE) derived by explicit discretisation of vector-kinetic equation (VKE), we also consider LBE derived by semi-implicit discretisation of VKE and compare the relaxation factors of both. We study the properties such as H-inequality, total variation boundedness and positivity of both the LBEs, and infer that the LBE due to semi-implicit discretisation naturally satisfies all the properties while the LBE due to explicit discretisation requires more restrictive condition on relaxation factor compared to the usual condition obtained from Chapman-Enskog expansion. We also derive the macroscopic finite difference form of the LBEs, and utilise it to establish the consistency of LBEs with the hyperbolic system. Further, we extend this LBM framework to hyperbolic conservation laws with source terms, such that there is no spurious numerical convection due to imbalance between convection and source terms. We also present a D2Q9 model that allows upwinding even along diagonal directions in addition to the usual upwinding along coordinate directions. The different aspects of the results are validated numerically on standard benchmark problems. • A semi-implicit lattice Boltzmann equation naturally satisfies stability properties like H-inequality, total variation boundedness and positivity. • Well-balancing of convection and source terms is handled easily in lattice Boltzmann framework. • A lattice Boltzmann model allows upwinding along diagonal directions apart from usual upwinding along coordinate directions. [ABSTRACT FROM AUTHOR]

• Influences of flow on hydrodynamic behavior of undulated beam are studied. • Mechanism of hydrodynamic behavior change in flow environment is revealed. • Performance of beam in flow environment is discussed, as well as a routing problem. • Loosely coupled partitioned algorithm is extended for self-propelled beam in flow environment. Undulated biomimetic propulsion has gained an extensive attention with upsurge of bionic applications. However, its performance in different flow environments is rarely discussed. In this paper, hydrodynamic behavior of an undulated beam in flow environments is studied, as well as its routing problem. The previously proposed loosely coupled partitioned algorithm is adopted. Motion of an undulated beam in still water is simulated to validate this algorithm. And then, hydrodynamic behavior of beam in flow environments with different directions and velocities is studied. It is found that velocity of beam is linearly affected by longitudinal flow and symmetric vortex structure still keeps. While transverse flow leads to the unequal amplitudes of velocity valley and crest, and symmetric vortex structure is lost. The influence of oblique flow could be regard as the combination of longitudinal and transverse flow components. Flow details are analyzed to reveal the mechanism of those hydrodynamic changes. Transverse flow component plays an important role. It significantly changes the pressure difference around beam and promotes the mixture of vortex. Besides, performance of beam in different flows and routing problem indicate that the straight path between the beginning and ending points is not always the best choice. [ABSTRACT FROM AUTHOR]

• Fire behaviour problems may be addressed by fully-physical models at different scales. • FireStar3D stands out among fire simulators in turbulence-radiation interaction modelling. • The new inlet condition allows fire-induced flow to occur while maintaining a crosswind. In addition to the experimental approach, wildfire modelling has been developed over the last decades to better understand the behaviour of wildfires and to propose new management tools to evaluate and reduce this natural hazard. This paper has twofold objective: (1) show how CFD simulation carried out using fully-physical models contributes to the understanding of wildfire behaviour, and (2) present new developments that were brought to FireStar3D – a fully-physical multiphase fire-simulator. The multiphase approach used in this class of models is briefly described, as well as the difficulties arising from the coupling between the various physical mechanisms of this multiscale problem. LES modelling and turbulence-radiation interaction used in FireStar3D is particularly detailed, as well as a new inlet boundary condition allowing to account for fire-induced flow while maintaining a prevailing crosswind far from the flaming zone. The benefits of multiphase CFD approach in addressing wildfire problems is demonstrated by considering three case studies of static and propagating vegetation fires having different length scales, which also highlights the model's potential in various configurations. [ABSTRACT FROM AUTHOR]

Knowledge of the bottom topography, also called bathymetry, of rivers, seas or the ocean is important for many areas of maritime science and civil engineering. While direct measurements are possible, they are time consuming, expensive and inaccurate. Therefore, many approaches have been proposed how to infer the bathymetry from measurements of surface waves. Mathematically, this is an inverse problem where an unknown system state needs to be reconstructed from observations with a suitable model for the flow as constraint. In many cases, the shallow water equations can be used to describe the flow. While theoretical studies of the efficacy of such a PDE-constrained optimisation approach for bathymetry reconstruction exist, there seem to be few publications that study its application to data obtained from real-world measurements. This paper shows that the approach can, at least qualitatively, reconstruct a Gaussian-shaped bathymetry in a wave flume from measurements of the free surface level at up to three points. Achieved normalised root mean square errors (NRMSE) are in line with other approaches. • We use PDE-constrained optimisation to reconstruct a Gaussian-shaped bathymetry in a wave flume. • We derive a continuous adjoint for the nonlinear shallow water equations in non-conservative form • Point measurements from two sensors are enough to produce a qualitatively correct reconstruction. [ABSTRACT FROM AUTHOR]

• The mechanism of deformation at the top position of the shell due to impact during high-speed water entry is studied. • Comparison and analysis of the differences in hydrodynamics and structural dynamics of shells with same material but different plastic properties during high-speed water entry are obtained. • The cavity evolution and motion characteristics of Shells with different materials is attained and discussed. • The entry of the shell into different solutions is discussed, and the difference between different solution is compared. To study the hydrodynamics and structural dynamics of the semi-sealed cylindrical shells with different material properties during water entry, based on the STAR-CCM+and ABAQUS collaborative simulation method, the numerical simulation with different material properties is conducted in this paper. The results show that shells with the same material but different plasticity have similar velocity and displacement, but their deformation and stress distribution on the top position differ significantly. The cavity evolution of shells with different densities is evidently different. The volume of secondary cavity of the shell with higher densities is larger, and the concentration force and stress distribution on the inner upper wall are also greater. When shells of the same material shell penetrate into solutions with different densities, the depth of the shell gradually increases as the solution density decreases. Solutions with different densities can fill the inner space of the shell for the first time, but not all solutions with different densities can fill the inner space of the shell for the second time, the volume of solutions with lower densities which entering into the inner space is larger. [ABSTRACT FROM AUTHOR]

• A 3D pseudo-potential multiphase model is developed. • The model is capable of achieving gas-liquid super-large density ratio. • The model is able to adjust surface tension independently of density ratio. • The numerical stability keeps well in the simulations with large density ratio and high Reynolds number. In this paper, an improved three-dimensional pseudo-potential multiphase flow model is proposed. A high-precision difference scheme is employed to improve the computational accuracy of the interaction forces to achieve super-large density ratio. The present model is verified to obtain two-phase density ratio up to hundreds of thousands for all selected equations of state, and the spurious currents can be suppressed to a relatively low level. A modification pressure tensor is introduced to implement a wide range of surface tension adjustments independently of the density ratio. The model is applied to simulate droplet impacts on a liquid film as well as droplet impacts on a dry surface. Numerical results show that the model still has good numerical stability in simulating complex fluid problems with very large density ratio, adjustable surface tension, high Reynolds number, or containing the wettable surface. In addition, to improve the computational efficiency, an efficient parallel algorithm based on graphics processing unit (GPU) is designed for the present model. A maximum speedup ratio of 687 times is obtained compared to the corresponding CPU-based serial algorithm, which can significantly accelerate the numerical simulation study. [ABSTRACT FROM AUTHOR]

Experimental tests accessing both fluid and structure behaviors are mandatory for a consistent and comprehensive assessment of fluid–structure interaction (FSI) numerical simulations. In this paper, recently published results of an experimental configuration of two in-line cantilever cylinders subjected to water cross-flow were considered: instantaneous fluid velocities measurements are available on several positions inside the test section, together with the cylinder vibrations. FSI simulations were performed by coupling Ansys Fluent (for the fluid domain) with Ansys Mechanical (for the solid domain). URANS simulations and Scale-Adaptive Simulations (SAS) were employed as CFD simulation approach. The structure displacements were taken into account through an Arbitrary Lagrangian–Eulerian approach. The fluid–structure coupling was 2-way explicit. Simulations were performed for two different water mass flow rates. For the highest one, vortex-induced resonance was observed experimentally. The numerical results show consistent agreement in terms of shedding frequency and velocity spectra behind the cylinders. The calculated vibration response is overall consistent, despite some underestimations, for the cylinders not featuring vortex-induced resonance; nevertheless, the experimentally observed vortex-induced resonance could not be reproduced by the numerical simulations. • Existing experimental results on FIV employed to assess CFD FSI simulations. • URANS and hybrid URANS/LES CFD approaches were tested: the latter proved superior. • Good agreement in terms of flow velocity spectra and mean profiles. • Coupled fluid-structure simulations were run to calculate the cylinder vibration. • Better agreement with exp. measurements for the second cylinder than for the first one. • A resonance was observed experimentally for the first cylinder at a given flow rate. • The resonance could not be predicted numerically. [ABSTRACT FROM AUTHOR]

• Interactions of a coaxial bubble pair in liquid metal have been performed. • Influence mechanism of magnetic field and wall on bubbles coalescence was revealed. • Attractive force of wake effect acting on tailing bubble is reduced by MHD effect. • Coalescence time of bubble pair is dependent to wall confinement ratio Cr and Ha. The motion and coalescence of a coaxial bubble pair rising in a liquid metal column under horizontal magnetic fields were numerically examined using the VOF method in this present paper. The MHD (Magnetohydrodynamics) effects on the characteristics of rise velocity, flow field, and coalescence process of bubble pair by considering various wall confinement ratios (Cr) were analyzed. The results indicate that the effects of magnetic field and wall confinement on the coalescence of the coaxial bubbles are non-monotonic. For smaller Cr , a higher initial rise velocity of the bubbles is generated by strengthening the counter-rotating toroidal vortices around bubbles in the initial stage, but the terminal rise velocity decreases in the stable stage. In the presence of the magnetic field, both the initial rise velocity and terminal rise velocity decrease. A horizontal magnetic field makes the flow field around the bubbles be anisotropic by weakening the toroidal vortices on both sides of the bubbles along the magnetic field direction, which also dampens the wake vortices of the leading bubble and thus reduces the attractive force of wake effect acting on the tailing bubble. On the other hand, the downward Lorentz force induced by the magnetic field on the top of the leading bubble suppresses its upward motion, which makes the tailing bubble collide with the leading bubble earlier. As the competition between the above two mechanisms varies with the magnetic field strength, the coalescence time of the bubble pair also changes accordingly. Particularly, a strong horizontal magnetic field tends to promote the bubbles coalescence under the wall effects and delay that when the wall effects are minor or negligible. For Ha =771, bubbles coalescence at Cr =2 is about 32 % earlier than that at Cr =4. [ABSTRACT FROM AUTHOR]

Our paper proposes an innovative approach for modeling Fluid–Structure Interaction (FSI). Our method combines both traditional monolithic and partitioned approaches, creating a hybrid solution that facilitates FSI. At each time iteration, the solid mesh is immersed within a fluid–solid mesh, all while maintaining its independent Lagrangian hyperelastic solver. The Eulerian mesh encompasses both the fluid and solid components and accommodates various physical phenomena. We enhance the interaction between solid and fluid through anisotropic mesh adaptation and the Level-Set methods. This enables a more accurate representation of their interaction. Together, these components constitute the Adaptive Immersed Mesh Method (AIMM). For both solvers, we utilize the Variational Multi-Scale (VMS) method, mitigating potential spurious oscillations common with piecewise linear tetrahedral elements. The framework operates in 3D with parallel computing capabilities. Our method's accuracy, robustness, and capabilities are assessed through a series of 2D numerical problems. Furthermore, we present various three-dimensional test cases and compare their results to experimental data. • A novel hybrid coupling method for FSI that takes the advantages of the partitioned approach, and retaining the advantages of the monolithic approach. • Ability to handle 2D/3D sharp membrane like geometries and interfaces through tetrahedral anisotropic unstructured finite elements.. • The level set method is used in the immersion of the solid mesh onto the fluid–solid mesh for interface tracking. • Variational Multi-Scale (VMS) stabilization for piece-wise linear finite elements to damp out spurious pressure oscillations and highly advective flows. • Moving Mesh Method (MMM) that considers the solid dynamics and helps track the FSI interface on the solid mesh. [ABSTRACT FROM AUTHOR]

This paper present the GRP-based GFM, which define the ghost fluid states by a local double-medium GRP established at the interface. The initial data of the GRP are linearly distributed, which are chosen by distance weighted least square fitting. The equations of the GRP have a source term associated with the tangential direction, which is necessary because of the Galilean invariance of the two-dimensional Euler equations. The intermediate states of the GRP are linearly distributed in numerical calculation. Modify the fluid states and their spatial derivatives along the normal direction of the interface in the real fluid regions near the interface by making use of the linearly distributed intermediate states. Then extend the fluid states and spatial derivatives in the real fluid regions near the interface to the ghost fluid regions by linear and constant extrapolating. The advantages of our proposed GRP-based GFM over the traditional RP-based GFM are as follows: (i) Reflect the effects of the source term associated with the tangential direction. (ii) Maintain the continuity of the material derivatives along the normal direction of the interface of pressure and normal velocity, and almostly eliminate the pressure and normal velocity mismatch errors near the interface. (iii) Comparing with choosing the initial data by bilinear interpolation, choosing the initial data by weighted least square fitting can improve the simulation results. (iv) Comparing with extending the ghost fluid states by solving the Eikonal equations iteratively, extending the ghost fluid states by linearly and constantly extrapolating can improve the numerical efficiency. Several typical numerical examples prove the superiority of our algorithm. [ABSTRACT FROM AUTHOR]

• Existing capacity models neglect the effects of flow sediment-storage variation. • Its effects on dam-break flooding and swash flows are numerically studied. • Simplification may lead to under-estimation of erosion or over-estimation of deposition, which considerably affects hydrodynamics. The capacity model based on the Exner equation has been widely used to simulate bed load sediment transport. However, most of their governing equations neglect a sediment storage term (∂ h C e / ∂ t), of which the impact on bed load transport simulation is unknown and needs to be better comprehended. This paper has split the capacity model into two sub-models: one with the sediment storage term and the other without the sediment storage term. The two sub-models are applied to simulate a series of typical bed load transport processes, such as dam-break flooding and swash flows. A comparison of their results is used to shed light on the effect of sediment storage term on flows and morphological evolutions. It is shown that for both dam-break flooding and swash flows, neglection of the inflow sediment storage may lead to under-estimation of bed erosion or over-estimation of bed deposition, which further affects the computed hydrodynamics greatly. Moreover, it is shown that including this factor can improve quantitative accuracy of sediment transport estimation. These indicate an important role of this factor and accordingly the present work provide a numerical justification for using sediment storage terms in capacity models. [ABSTRACT FROM AUTHOR]

The continuous development of machine learning algorithms has stimulated the technological revolution on turbulence modeling for Reynolds-averaged Navier–Stokes (RANS) simulations. In this paper, a computable transition-enabled turbulence model is developed with the aid of an artificial neural network (ANN), which maps the relation between the mean flow variables from the shear stress transport (SST) model on coarse grid and the turbulent viscosity from SST- γ model on fine grid. It turns out that the ANN model can predict the aerodynamic integral quantities, transition onset location, laminar separation bubble structure, streamwise velocity distribution, etc. with superior accuracy and robustness for subsonic and moderate transonic airfoil flows. Meanwhile, the ANN model can significantly improve the convergence property with a much higher convergence speed of the model equation in comparison with traditional transition-enabled RANS model. Moreover, due to the lack of solving RANS model equations and use of grid interpolation technology, the computation speed of this ANN model is improved by a factor of about six over the conventional benchmark model. Therefore, the present computable ANN model provides a new perspective for high-efficiency simulation of transition-characterized flows in engineering applications. • A new transition-turbulence modeling strategy is suggested based on artificial neural network (ANN). • The ANN algorithm provides a corrector for the eddy viscosity in full-turbulence model. • The ANN model is intended to mimic the eddy viscosity in transition-enabled model. • No turbulence model equations need to be solved while retaining a good generalization property. • Grid interpolation and frozen correction help improve the computation efficiency while ensuring the simulation accuracy. [ABSTRACT FROM AUTHOR]

In this paper, a new method to model solidification of thin liquid films is proposed. This method is targeted at applications like aircraft icing and tablet coating where the formation of liquid films from impinging droplets on a surface form a critical part of the physics of the process. The proposed model takes into account the (i) unsteadiness in temperature distribution, (ii) heat transfer at the interface between the solid and the surface, (iii) volumetric expansion/contraction and (iv) the liquid thin-film behaviour, each of which are either partly or fully ignored in existing models. The liquid thin-film, modelled using the Discrete Droplet Method (DDM), is represented as a collection of discrete droplets that are tracked in a Lagrangian sense. The height of the liquid film is estimated as a summation of Gaussian kernel functions associated with each droplet. At each droplet location, a solid height is also computed. The evolution of the solid height is governed by the Stefan problem. The flow of the liquid thin-film is solved just as in the case of DDM, while also taking into consideration the shape of the solidified region lying beneath the droplet. The results presented in this work show the reliability of the proposed model in simulating solidification of thin-films and its applicability to complex problems such as ice-formation on aircraft wings. The model has been verified for canonical problems that have analytical solutions. For the more complex problems of icing, the results of the model are compared with data from literature, without considering a background air flow. The comparison can be improved by coupling this model with suitable air flow solvers, as shown in the final test case. • A novel model for solidification in liquid thin-film flows over substrates • The model accounts for - unsteadiness in temperature distribution, heat transfer at interfaces, volumetric change, coupling with thin-film flow. • The model is validated through a series of test cases of increasing complexity. • Ice formation on a circular conductor and an aircraft wing illustrate the effectiveness of the model. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel fluid–structure interaction framework based on the smoothed particle hydrodynamics model for fluids and a recently developed constitutively informed particle dynamics model for solids. We develop a new method for coupling these approaches to expand the fluid–structure simulation framework to include crack propagation failure in the solid. Several benchmark problems have been simulated to validate the fluid and solid models separately as well as the coupled model. We then apply this coupled approach to model brittle failure of a notched bar impacted by a fluid. We study the effect of various parameters such as height of the obstacle and location of the notch on its fracture. • Coupling of SPH with Constitutively informed particle dynamics demonstrated. • Ability to model fracture of the solid in FSI problems demonstrated. • Role of notch location on fracture behavior is studied. • General constitutive behavior of the solids can be modeled. [ABSTRACT FROM AUTHOR]

We describe a data-driven, multiscale technique to model reactive wetting of a silver–aluminum alloy on a Kovar™ (Fe-Ni-Co alloy) surface. We employ molecular dynamics simulations to elucidate the dependence of surface tension and wetting angle on the drop's composition and temperature. A design of computational experiments is used to efficiently generate training data of surface tension and wetting angle from a limited number of molecular dynamics simulations. The simulation results are used to parameterize models of the material's wetting properties and compute the uncertainty in the models due to limited data. The data-driven models are incorporated into an engineering-scale (continuum) model of a silver–aluminum sessile drop on a Kovar™ substrate. Model predictions of the wetting angle are compared with experiments of pure silver spreading on Kovar™ to quantify the model-form errors introduced by the limited training data versus the simplifications inherent in the molecular dynamics simulations. The paper presents innovations in the determination of "convergence" of noisy MD simulations before they are used to extract the wetting angle and surface tension, and the construction of their models which approximate physio-chemical processes that are left unresolved by the engineering-scale model. Together, these constitute a multiscale approach that integrates molecular-scale information into continuum scale models. • Constructed a data-driven wetting model from molecular dynamics simulations. • Studied wetting of molten silver-aluminum alloy on a Kovar™ substrate for brazing. • Performed molecular dynamics simulation to predict surface tension & wetting angle. • Calibrated probabilistic, data-driven surrogate model using limited training data. • Integrated wetting model into engineering-scale finite element brazing model. • Compared model to experiment, identifying missing physics in simulations. [ABSTRACT FROM AUTHOR]

This paper compares two different delayed detached-eddy simulation (DDES) techniques, namely iDDES and l 2 - ω -DDES. Their performance is investigated with and without combustion. While iDDES limits the dissipation term of the turbulent kinetic energy equation, l 2 - ω -DDES confines its production term. In this way, both models achieve that resolved turbulence is enhanced in regions of separated flow. On the other hand, the models show significant differences. In a first step this is investigated using three non-reactive test cases. While here the first-order moments are in a fairly good agreement, the second-order moments exhibit slight differences. Despite the similarities in first- and second-order moments, the instantaneous flow fields differ considerably with the iDDES displaying finer vortex structures. This is caused by different levels of eddy viscosity. These disparities are even more pronounced in case of a laboratory-scale rocket combustion chamber, where strong differences in quantities as the wall heat flux are observed. This clearly demonstrates an impact on the combustion process. • First comparison of production- and dissipation-limited DDES methods for combustors. • Theoretical and practical analysis shows higher eddy viscosities of the l 2 - ω -DDES. • Modeled parts of turbulent quantities are higher for l 2 - ω -DDES than for iDDES. • For all cases, l 2 - ω -DDES is closer to local equilibrium than iDDES. • l 2 - ω -DDES shows good agreement with experimental heat flux of the PennState combustor. [ABSTRACT FROM AUTHOR]

In this paper, we consider developing high-order temporal integration schemes for the unsteady incompressible Navier–Stokes equations in bounded two-dimensional domain subjected to the periodic boundary conditions. Utilizing the k -step (k = 3 , 4 , 5) backward differentiation formula (BDF) coupled with the implicit–explicit (IMEX) treatment of the nonlinear convective term in an anti-symmetry form, a class of IMEX-BDF k schemes up to fifth-order in time are constructed and analyzed. By imposing a zero-mean constrain on the finite-dimensional space for the pressure, the proposed numerical schemes are proven to be uniquely solvable. Based on the recent theoretical framework consisting of a class of discrete orthogonal convolution kernels, rigorous L 2 norm error estimates for both the velocity and the pressure are established by using a novel divergence free projection system. The proposed schemes are then implemented in two benchmark experiments, including a Taylor–Green vortex problem and a double shear layer flow at various high Reynolds numbers. Numerical results demonstrate the expected solution accuracy and the computational effectiveness in simulating the realistic flow dynamics. • We consider developing high-order temporal integration schemes for the incompressible Navier–Stokes equations. • We introduce a class of discrete orthogonal convolution kernels to develop a unified framework for the L 2 norm convergence analysis. • Extensive benchmark experiments are performed to show the effectiveness of the high-order IMEX-BDF schemes. [ABSTRACT FROM AUTHOR]

Computational fluid dynamics (CFD), in particular applied to turbulent flows, is a research area with great engineering and fundamental physical interest. However, already at moderately high Reynolds numbers the computational cost becomes prohibitive as the range of active spatial and temporal scales is quickly widening. Specifically scale-resolving simulations, including large-eddy simulation (LES) and direct numerical simulations (DNS), thus need to rely on modern efficient numerical methods and corresponding software implementations. Recent trends and advancements, including more diverse and heterogeneous hardware in High-Performance Computing (HPC), are challenging software developers in their pursuit for good performance and numerical stability. The well-known maxim "software outlives hardware" may no longer necessarily hold true, and developers are today forced to re-factor their codebases to leverage these powerful new systems. In this paper, we present Neko, a new portable framework for high-order spectral element discretization, targeting turbulent flows in moderately complex geometries. Neko is fully available as open software. Unlike prior works, Neko adopts a modern object-oriented approach in Fortran 2008, allowing multi-tier abstractions of the solver stack and facilitating hardware backends ranging from general-purpose processors (CPUs) down to exotic vector processors and FPGAs. We show that Neko's performance and accuracy are comparable to NekRS, and thus on-par with Nek5000's successor on modern CPU machines. Furthermore, we develop a performance model, which we use to discuss challenges and opportunities for high-order solvers on emerging hardware. • We introduce Neko, a modernized framework for high-fidelity CFD simulations. • We reveal Neko's inner implementation details and design decisions. • We develop a performance model, which we validate and use to project performance. [ABSTRACT FROM AUTHOR]

On the basis of previous work, we propose a phenomenological computable Boltzmann model equation synchronously involving polyatomic molecular internal energies, dissociation and recombination effects for multicomponent gases in this paper. Here, the distribution functions of each species have nine independent variables, which are time, physical space, molecular velocity, rotational energy and vibrational energy, if this component is a polyatomic gas. In this model equation, the concept of 'chemical reaction rate' is introduced in the chemical collision term to characterize the affect of chemical reactions. In order to make this complex model equation being 'computable', reduced distribution functions are adopted to get rid of two independent variables about rotational energy and vibrational energy of polyatomic component. We prove the conservation of this model equation, and then numerically solve it by the framework of gas-kinetic unified algorithm (GKUA), which is one kind of discrete velocity method (DVM). Here, non-catalytic boundary condition is adopted. Finally, a simple hypersonic flow around a cylinder with Mach number being 24.85 is numerically simulated to verify this model equation. In this case, four different components and eight chemical reactions are considered. It is shown that, this proposed Boltzmann model equation has the potential to be used to simulate thermochemical non-equilibrium effects of hypersonic flows covering various regimes. • A computable kinetic model involving polyatomic molecular internal energies and chemical reaction effects, including dissociation and recombination, is presented for hypersonic flows of multicomponent mixed gases. • The conservation laws of mass, momentum and energy of this model are analyzed for each component and entire system. • The gas-kinetic unified algorithm (GKUA) is developed to numerically solve the proposed kinetic model and is preliminarily verified by comparing its results with those of the DSMC method for a hypersonic flow case. [ABSTRACT FROM AUTHOR]

This paper proposes a novel evolution equation for simulating conjugate heat transfer (CHT) phenomena in an immersed boundary-lattice Boltzmann (IB-LB) framework. Unlike the existing LB methodologies that reconstruct the unknown energy distribution function or add an additional source term to satisfy the interfacial boundary conditions, the proposed novel approach introduces a unified governing equation for different medium present in the computational domain via partially saturated computational cells (PSC) method. The PSC methodology offers a volume-of-body based diffuse-interface IB-LB formulation which efficiently implements the conjugate boundary conditions over the complex solid–fluid interface that are not aligned with the underlying Cartesian grid. The present work reveals that the proposed algorithm is first-order accurate in space irrespective of the boundary being straight or curved. Further, it illustrates the development and robustness of the solver for a wide range of non-trivial benchmark problems encompassing free, forced, and mixed convection phenomena. To the best of authors' knowledge the proposed algorithm is also the first known instance of the use of PSC approach for CHT problems. • A novel governing equation for simulating conjugate heat transfer problems using PSC. • Unified evolution equation for conjugate condition at complex solid–fluid interface. • PSC is first-order accurate and robust for free, forced and mixed convection problems. [ABSTRACT FROM AUTHOR]

• Propose an improved SST turbulence model which combines the structural parameter with the ratio of the turbulence generation term to the dissipation term and imposes a mixing function to correct the logarithmic and wake parts of the region. A goal in modeling the turbulent flows in computational fluid dynamics is to find an empirical yet universal model to address the complex scenarios. Menter's Shear Stress Transfer (SST) [1] is a Reynolds-Averaged Navier-Stokes (RANS) based two-equation turbulence model and has been one of the most widely used turbulence models for numerical simulation of viscous flows. However, in some practical cases on supersonic, the standard SST model shows unsatisfactory prediction of flow separation and the often underestimation of Reynolds stress. The error mainly comes from the inappropriate use of Bradshaw's assumption which is proposed under turbulent kinetic energy (TKE) equilibrium flow conditions. This paper proposes an improved SST turbulence model which combines the structural parameter with the ratio of the turbulence generation term to the dissipation term and imposes a mixing function to correct the logarithmic and wake parts of the region. Several supersonic test cases are carried out to verify the new model. The calculation results show that the new model exhibits better performance in capturing the separation zones than the baseline model (BSL) and the standard SST model. [ABSTRACT FROM AUTHOR]

This paper proposes a high-order pseudo arc-length method (PALM) for multi-medium flows with strong robustness, stability, and positivity preservation for solving one- and two-dimensional compressible Euler equations. The main idea of the proposed scheme is to add an additional arc-length constraint equation to the original control equation and map it to the uniform orthogonal arc-length space. We discretize the space with high accuracy by using the high-order weighted essentially non-oscillatory (WENO) interpolation reconstruction, which overcomes the difficulty of constructing the high-order format due to the physical space deformation caused by the grid movement. The application scope of the positivity-preserving algorithm is further expanded, and the positivity-preserving limiter of the high-order WENO pseudo arc-length adaptive method in the coordinate system of the arc-length calculation is constructed and proved, solving the problem of the negative density and pressure caused by the interaction between a strong shock wave and a strong sparse wave. For grid motion after interpolation of the level set function, a third-order non-conservative interpolation scheme is offered to ensure the interface capture accuracy. Finally, combined with level set interface tracking and the real ghost fluid method interface-processing techniques, the algorithm is applied to calculate multi-medium flows. Numerical examples show that the PALM almost eliminates the mass loss near the interface and maintains the high-accuracy and high-resolution characteristics of the algorithm when dealing with extreme problems such as low density, low pressure, strong shock waves, or strong sparse waves. • Propose a high-order pseudo arc-length method (PALM) for multi-medium flows. • A positivity-preserving flux limiter in the coordinate system of arc-length calculation is constructed. • A third-order non-conservative interpolation scheme is proposed. • Effectively solve the problem of extreme explosion and shock. [ABSTRACT FROM AUTHOR]

In this paper, a multiple-relaxation-time lattice Boltzmann (LB) approach is developed for the simulation of three-dimensional (3D) liquid–vapor phase change based on the pseudopotential model. In contrast to some existing 3D thermal LB models for liquid–vapor phase change, the present approach has two advantages: for one thing, some gradient terms, such as the gradient of volumetric heat capacity and the Laplacian term of temperature, that must be computed with finite-difference scheme in previous works is not needed for the present thermal model. For another, the current model is constructed based on the seven discrete velocities in three dimensions (D3Q7), making it more efficient and much easier to be implemented. Also, based on the scheme proposed by Zhou and He (1997), a pressure boundary condition for the D3Q19 lattice is proposed to model the multiphase flow in open systems. This model is then validated by considering the temperature distribution in a 3D saturated liquid–vapor system, the d 2 law, the droplet evaporation on a heated surface and the nucleate boiling. It is observed that the numerical results fit well with the analytical solutions, and the results of the finite difference method or the experimental data. Our numerical results indicate that the present approach is reliable and efficient in dealing with the 3D liquid–vapor phase change. • An efficient LB model to simulate 3D liquid–vapor phase change is proposed. • The current model is constructed based on the D3Q7 lattice. • This method needs not calculate the density gradient. [ABSTRACT FROM AUTHOR]

• As the Mach number increases from 2.0 to 5.0, the dynamic response changes from limit cycle oscillations to complex states. • As dynamic pressure increases, the dynamical response changes from complex states to limit cycle oscillations. • The first-order bending mode frequency is dominant and remains constant over time. • The variation law of the flow field with the oscillation of the drag-reduction spike is summarized. The drag-reduction spike is widely employed in the testing of hypersonic vehicles owing to its remarkable ability to reduce drag and heat. Further investigation into the aeroelastic characteristics and mechanisms of the drag-reduction spike will offer a valuable reference for the refined design of its aerodynamics and structure. In this paper, based on the in-house high-order accurate CFD/CSD coupling analysis method, the variation law and mechanism of the nonlinear aeroelastic characteristics of the drag-reduction spike under different Mach numbers and dynamic pressures are studied. The results indicate that the nonlinear dynamic response of the drag-reduction spike transitions from limit cycle oscillations to more complex oscillatory characteristics as the Mach number increases from 2.0 to 5.0. Simultaneously, it is observed that the amplitude of the structural response also increases correspondingly. The primary factor contributing to this phenomenon is the elevated Mach number, which intensifies the interaction of unsteady aerodynamic loads on the surface of the spike. As a result, the location of the separation points and the structure of the separation vortex on the upper and lower surfaces become significantly asymmetric. Furthermore, as the dynamic pressure increases, the nonlinear dynamic response transitions from a complex characteristic to a stable limit cycle oscillation, accompanied by a corresponding increase in the structural amplitude. In both cases, the dynamical characteristics are mainly dominated by the first-order bending mode, and the vibration frequency remains consistent over time. Besides, the variation law of the flow field with the oscillation of the drag-reduction spike is summarized. As the spike is displaced, the complexity of the separation vortex and the intensity of the reattachment shock wave on the offset side gradually decrease, while the reverse is true on the other side. Meanwhile, a vortex is generated on the blunt body on the offset side of the spike, and the vortex region becomes larger as the offset increases. [ABSTRACT FROM AUTHOR]

The prediction of compressible nonisothermal flows of viscoelastic fluids is important in many industrial processes. Until relatively recently, there was a lack of tractable thermodynamically consistent mathematical models for this class of flows. In this paper a stabilised finite element scheme is presented for the models developed by the authors Mackay and Phillips (2019) which incorporates compressibility and nonisothermal effects. Numerical results are presented for variants of a couple of benchmark problems: the lid driven cavity and the natural convection problems. The temporal discretisation is based on the Taylor–Galerkin method. A compressible version of the discrete elastic viscous split stress (DEVSS) formulation is used to stabilise the numerical scheme. The combined and separate influence of compressible, viscoelastic and thermal effects on the characteristics of these benchmark flows is studied for the first time. • Numerical schemes for compressible, nonisothermal viscoelastic flows are presented. • The influence of stabilisation methods on convergence is explored. • The influence of compressible, viscoelastic and thermal effects is studied. • For lid-driven cavity flow, viscoelasticity increases elastic energy while compressibility decreases it. • Viscoelasticity reduces overall heat transfer in a convection cell. [ABSTRACT FROM AUTHOR]

This paper examines the parallel efficiency of an ARM-based single board computing cluster made of 16 Raspberry Pi 4 and 8 Nvidia Jetson Nano Single Board Computer, considering both CPU and GPU parallel implementation of CFD applications. It is found that the parallelization scales up to 16 Raspberry Pi 4 and 8 Nvidia Jetson Nano (maximum available on the current cluster). Moreover, it is shown that regarding the computation time, about 12 SBC are as fast as a classical computing workstation. Finally, it is shown that such cluster are energy efficient considering CFD applications. • Single board computers with ARM processors are very efficient for CFD applications. • Parallel computing on single board computing cluster is scalable on gigabit LAN. • A single board computing cluster has a Power Usage Effectiveness near 1. [ABSTRACT FROM AUTHOR]

• One-step to consistent high order in time and space without Runge-Kutta(RK) methods. • High efficiency that computing speed is more than s /CFL Full/RK times as much as same order WENO with s -stage RK method. • Achieving exact solution in linear cases and performing better in nonlinear cases when CFL→1. • High resolution with excellent shock-capturing capacity. • Entropy condition automatically satisfied without extra artificial viscosity. Different from the spatial semi-discrete WENO schemes based on RK method in time, this paper presents a fully-discrete scheme with consistent high order in time and space based on solution formula method. Analyzing the error composition of the framework, we obtain two core steps of discretization for constructing high-order schemes: initial value reconstruction and flux reconstruction. During the reconstruction, we apply the Newton interpolation with WENO thought and newly designed limiters to maintain robustness. Since the new method uses WENO reconstruction on fully-discrete framework, we name the new scheme as Full-WENO. With characteristics projection and Strang split technique, we extend the method to multi-dimensional Euler equations under curvilinear coordinates. The new scheme has following advantages: (1) One-step to consistent high order in time and space with excellent shock-capturing capacity; (2) Achieving exact solution in linear cases and performing better in nonlinear cases when CFL→1, and even can be stably implemented under CFL=1; (3) High resolution, especially for long-time evolution problems; (3) High efficiency, Full-WENO is s times faster than classical WENO with s -stage RK method under same computing condition; (4) Entropy condition automatically satisfied without additional artificial numerical viscidity. Numerical experiments contain tests of accuracy order, linear and nonlinear scalar equation, 1D and 2D Euler equations, efficiency, and sonic point. All of these verify the new scheme is equipped with the merits of high order, high resolution, and high efficiency. [ABSTRACT FROM AUTHOR]

• An approach used to calculate the solid volume fraction in a cubic grid is proposed. • The solid is approximated by a certain number of triangular planes in this approach. • The approach has higher efficiency than common method without losing accuracy. • The PSM-LBM simulations are also conducted to further validate this approach. Within the LBM (Lattice Boltzmann Method), PSM (Partially Saturated Method) is a quite straightforward approach for dealing with solid boundaries. Additionally, PSM also has the advantages of mass-conserving and no fresh node problem. There have been numerous successful implementations of PSM in processing the fluid-solid interactions in previous investigations. In PSM, calculating the solid volume fraction in cubic LBM cells near solid boundaries is an indispensable prerequisite. However, the methods adopted in the previous work have quite low efficiency in determining the solid fraction for complex boundaries. Additionally, most of the PSM-LBM investigations concentrate on the boundary with rather simple geometry (e.g., the sphere in 3D and the circle in 2D). Therefore, an approach based on the projection method is proposed in this paper to accurately and efficiently determine the solid volume fraction of complex boundaries in a cubic cell. To demonstrate the capability of our proposed approach, the calculation results of the solid volume fraction are compared with the theoretical solution of a spherical solid and the subdivision method. The comparison results demonstrate that this approach is up to 10 times more efficient than the subdivision method for the same level of accuracy. Subsequently, the proposed approach is incorporated into PSM-LBM to simulate the flow over a stationary obstacle with a relatively regular shape (including sphere, cube, and ellipsoid) and the quite complex geometry (the rearview mirror) for further verifying the ability of the proposed approach. The fairly favorable consistency between the current simulation results and the literature data can ulteriorly validate the feasibility of this approach in processing fluid-solid interaction involving complex boundaries. [ABSTRACT FROM AUTHOR]

Accurate high-speed flow simulations of practical interest require numerical methods with high-resolution properties. In this paper, we present an extension and demonstration of the high-accuracy Gradient-based reconstruction and α -damping schemes introduced by Chamarthi (2022) for simulating high-speed flows in generalized curvilinear and dynamic mesh domains with the freestream preservation property. In the first part of this paper, the algorithms are detailed within the generalized curvilinear coordinate framework, with a focus on demonstration through stationary and dynamic mesh test cases. It has been shown both theoretically and through the use of test cases that the conservative metrics, including their interpolation to cell interfaces, must be numerically computed using a central scheme that is consistent with the inviscid flux algorithm to achieve the freestream preservation property. The second part of the paper illustrates the efficacy of the algorithm in simulating supersonic jet screech by displaying its capability to capture the screech tones and accurately characterize the unsteady lateral flapping mode of a Mach 1.35 under-expanded supersonic jet, in contrast to the WENO-Z scheme which fails to do so at the same grid resolution. In the final part of the paper, the parallelizability of the schemes on GPU architectures is demonstrated and performance metrics are evaluated. A significant speedup of over 200 × (compared to a single core CPU) and a reduction in simulation completion time to 34.5 h per simulation were achieved for the supersonic jet noise case at a grid resolution of 13 million cells. • MEG6/MIG4 are extended to curvilinear domains satisfying freestream preservation property • MEG6 and MIG4 outperformed WENO-Z in resolving unsteady aspects of Mach 1.35 choked supersonic jet • OpenACC GPU implementation of MEG6 resulted in ≈ 200 × speedup compared to single-core CPU [ABSTRACT FROM AUTHOR]

Numerical simulations are extensively used as a predictive tool to better understand complex air flows and pollution transport on the scale of individual buildings, city blocks and entire cities. Fast-running Non-Intrusive Reduced Order Model (NIROM) for predicting the turbulent air flows has been proved to be an efficient method to provide numerical forecasting results. However, due to the reduced space on which the model operates, the solution includes uncertainties. Additionally, any computational methodology contributes to uncertainty due to finite precision and the consequent accumulation and amplification of round-off errors. Taking into account these uncertainties is essential for the acceptance of any numerical simulation. In this paper we combine the NIROM method with Data Assimilation (DA), the main question is how to incorporate data (e.g. from physical measurements) in models in a suitable way, in order to improve model predictions and quantify prediction uncertainty. Here, the focus is on the prediction of nonlinear dynamical systems (the classical application example being weather forecasting). DA is an uncertainty quantification technique used to incorporate observed data into a prediction model in order to improve numerical forecasted results. The Reduced Order Data Assimilation (RODA) model we propose in this paper achieves both efficiency and accuracy including Variational DA into NIROM. The model we present is applied to the pollutant dispersion within an urban environment. • We developed a Reduced Order with variational Data Assimilation (RODA) Model. • RODA Model improves both accuracy and efficiency of predictions. • The employment of ROM in the DA cycle improves the efficiency of this last one. • DA incorporates data from physical measurements in ROM improving its accuracy. • The RODA model is applied to the pollutant dispersion within an urban environment. [ABSTRACT FROM AUTHOR]