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• 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]

• 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]

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]

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]

Vehicle wading problems have received increasing attention from the automotive community in recent years because of the prosperous developments of electric vehicles, for which the performance of water tightness can be more important than conventional fuel vehicles. This paper presents an attempt to simulate vehicle wading problems based on an entirely meshless framework by using Smoothed Particle Hydrodynamics (SPH). First of all, an easy-to-implement but effective strategy is proposed to prevent the penetration between fluid particles and a wall boundary modeled by a set of solid particles when the distribution quality of the solid particles is poor. Subsequently, a comparative study is conducted to assess the feasibility and applicability of the SPH and Finite Volume (FV) methods in solving vehicle wading problems. Furthermore, the wading dynamics of a vehicle passing a puddle under different combinations of wading speeds and accumulating water depths is also investigated and discussed in detail by using the SPH method. It is suggested that the SPH method can be regarded as a potential candidate for solving vehicle wading problems, especially for those situations where the free-surface evolution during the wading process is particularly concerning. • Strategy to prevent particle penetration between fluid and solid is proposed. • Comparison of the SPH and FV methods in solving vehicle wading is performed. • Investigation of a vehicle wading in a puddle for various conditions is provided. • The SPH method shows great potential in solving vehicle wading problems. [ABSTRACT FROM AUTHOR]

Mesh quality is critical for the numerical accuracy of CFD (Computational Fluid Dynamics). Although various techniques have been developed to improve mesh applicability to complex flows, r-adaptive methods have received far too little attention. This paper introduces an r-adaptive algorithm based on the self-organizing maps (SOM) of Kohonen and applies it to unsteady CFD applications using the Discontinuous Galerkin (DG) method. Inspired by the properties of the DG method, the numerical discontinuity over the element interface is quantified as an adaptation indicator. The method requires only one adaptation, followed by solution projection onto the new mesh to save computational costs in unsteady cases. A significant advantage of this method is its higher efficiency without solving complex equations during the adaptation. The performance of the developed mesh adaptation algorithm is tested on the steady laminar viscous flow past a circular cylinder at R e = 40 and the unsteady laminar viscous flow past a circular cylinder at R e = 100 and two circular cylinders in a side-by-side arrangement at R e = 200. Significant improvements in flow contours and coefficients are obtained after adaptation. • The SOM method is adopted for unstructured mesh r-adaptation with the DG method. • The method avoids auxiliary mesh PDEs in traditional r-adaptation methods. • A one-time adaptation in unsteady cases saves computational costs. • The improvement of results in CFD applications validates method performance. [ABSTRACT FROM AUTHOR]

With ITER, the largest tokamak ever built, and the growing number of fusion energy startups in the world, the need for numerical simulations has never been more crucial to progress towards the successful operation of fusion reactors. From fundamental plasma physics to engineering, a hierarchy of models exists from high-fidelity (gyro-)kinetic models in (5D) 6D to 0D fluid transport models. In this paper, we review the state-of-the-art of 3D turbulence fluid simulations in edge tokamak configurations. The widely used drift-reduced Braginskii equations are introduced together with the dedicated boundary conditions modelling plasma wall interactions. If until recently most of the models were focused on electrostatic turbulence driven by interchange-like instabilities, in recent years models have incorporated electromagnetic effects allowing fluctuations of the magnetic field. Specific features of the edge plasma configurations, which make these equations specially challenging to resolve and stressful for the numerical methods, are detailed. In particular, the strong anisotropy of the flow as well as the complex geometric characteristics lead to the development of dedicated discretization schemes and meshing, which are implemented in state-of-the-art codes reviewed here. It appears that the latter can be differentiated by their mesh construction as well by the manner in which they handle parallel gradients (aligned or not along the magnetic field). The review shows that no consensus on the optimal combination between meshing and discretization schemes, if it exists, has been found. Finally, examples of recent achievements show that 3D turbulence simulations of medium-sized tokamaks are currently achievable, but that ITER-size tokamaks and thermonuclear plasmas still require significant progress. • Focus on key challenges in simulating edge plasma turbulence in tokamak. • Fluid mathematical models for tokamak plasma simulation. • Synthesis on advanced numerical methods, discretization and meshing. • State-of-the-art turbulence codes to simulate edge tokamak plasmas turbulence. • Recent key achievements showing the capabilities of turbulence codes to address tokamak relevant physics. [ABSTRACT FROM AUTHOR]

This paper presents a stable and highly accurate numerical tool for computing river flows in urban areas, which is a first step towards a numerical tool for flood predictions. We start with the (linearized) well-posedness analysis by Ghader and Nordström (2014), where far-field boundary conditions were proposed and extend their analysis to include wall boundaries. Specifically, we employed high-order Summation-by-parts (SBP) finite-difference operators to construct a scheme for the Shallow Water Equations. We also developed a stable SBP scheme with Simultaneous Approximation Terms that impose far-field and wall boundaries. Finally, we extended the schemes and their stability proofs to non-Cartesian domains. To demonstrate the strength of the schemes, we performed computations for problems with exact solutions to obtain second, third, and fourth (2, 3, 4) convergence rates. Finally, we applied the 4 t h -order scheme to steady river channels, the canal (or flood-control channel simulations), and dam-break problems. The results show that the imposition of the boundary conditions is stable, and the far-field boundaries cause no visible reflections at the boundaries. • Derivation of linearly well-posed boundary conditions for the SWE. • Development of stable SBP-SAT schemes with these boundary conditions. • Numerical verifications of the stability of the boundary treatment. [ABSTRACT FROM AUTHOR]

In this paper, we present a cylindrical discontinuous Galerkin method for compressible flows in axisymmetric geometry. The axisymmetric Euler equations in geometric flux form are discretized by the Runge–Kutta DG method. To ensure conservativeness when using limiters developed for the 1- and 2-dimensional planar problems, the basis is modified from the Legendre polynomials such that the non-zero order moments in each cell do not contribute to the cell average value. Several 1- and 2-dimensional cylindrical tests are implemented and compared with the reference results. The present method exhibits the expected order accuracy in smooth problems and has a good performance in some challenging tests such as Noh problem and Sedov problem. • A cylindrical DG method to solve axisymmetric Euler equations in geometric flux form is developed. • The basis functions are modified to ensure conservativeness when using limiters. • A minimal region near the symmetric axis is removed to avoid the influence of the singularity. [ABSTRACT FROM AUTHOR]

The parabolized stability equations (PSE) are a widely used, efficient method to calculate the evolution of streamwise traveling instabilities in spatially developing, weakly nonparallel flows. Although the PSE are very economical, computational time can be significant due to the repeated solution of linear systems of equations in each marching step. The linear systems of equations are typically solved by LU factorization because of the moderate size and the sparsity of the matrices. In this paper, instead of repeated calculation of the LU factorization, a single LU factorization is calculated in each marching step and used as a preconditioner for an iterative solver. Numerical experiments are conducted on the plane-marching (3D) incompressible PSE, nonlinear PSE (NLPSE) with explicit discretization of the nonlinear terms, and NLPSE with implicit treatment of the nonlinearities. It is shown that the time spent on the solution of the linear systems of equations was reduced by a factor of 2.5, 4.5–7.5, and 20–60 for the three cases, respectively. The only requirement of the proposed numerical techniques is that the solution varies slowly in the marching direction; therefore it is expected to be applicable to similar boundary layer stability problems or slowly varying parabolic partial differential equations. This is supported by the fact that the numerical method was applied to the Boundary Region Equations (BRE) and the line-marching (2D) PSE, the latter being a much smaller problem than its plane-marching counterpart. In these cases, a factor of 50% and 15–30% decrease in the net time of the linear equation solution is reported, respectively. • A simple method is outlined to accelerate the solution of plane marching PSE. • The solution of both the linear and the nonlinear plane marching PSE can be accelerated. • The efficient solution method renders the implicit discretization of the nonlinear terms feasible. • The applicability of the method to slowly varying equations is demonstrated on the BRE. [ABSTRACT FROM AUTHOR]

Predictive sampling of compressible flows is an important aspect of aerodynamic design, analysis, and optimization. The process is usually done by generating flow fields from computational fluid dynamics (CFD) simulations and solving governing evolution equations, from which quantities of interest (QoI) are obtained by post-processing. With this study, we propose a data-driven approach for the predictive sampling of compressible flows around airfoils. This paper demonstrates the potential of generative adverserial networks (GANs), particularly the Pix2Pix model, to predict supersonic flow fields around airfoils. Building upon the similarities between our generator architecture and FlowGAN, which also employs the Pix2Pix model, our work extends the capabilities of FlowGAN to encompass supersonic flows and higher-resolution predictions. Our methodology introduces a multi-variable prediction framework, enabling the simultaneous prediction of various flow variables, including pressure, velocity, and density. We achieve the generation of flow fields with a relative error of less than 1.5%. We utilize the same framework to train a model capable of generating synthetic schlieren images, exhibiting a similarity structure index greater than 0.97, underscoring the high-fidelity generation capacity of our model. Addressing the challenges of generalization to unseen Mach numbers and angles of attack, we adopt transfer learning. By fine-tuning a pre-trained model on a limited number of examples from the unseen parameters, we obtain an improved prediction of shock wave positions. Furthermore, we present a practical application of our methodology by reconstructing flow fields from schlieren images. This application could prove valuable in real-world scenarios, providing a useful tool for studying and comprehending complex flow phenomena. • GANs, in particular, the Pix2Pix model are explored to predict supersonic flow fields around airfoils. • A multi-variable high-resolution prediction framework is implemented and succeeds in generating flow fields with a relative error of less than 1.5%. • The same framework is used tp train a model to generate synthetic Schlieren images with a similarity structure index greater than 0.97. • To overcome the limitations of the model to generalize to some unseen Mach numbers and angles of attack, transfer learning is used. • Flow fields are reconstructed from schlieren images, providing a practical and useful tool for studying and understanding complex flow phenomena in real-world scenarios. [ABSTRACT FROM AUTHOR]

At equilibrium state of a two-phase fluid system, the chemical potential is constant and the velocity vanishes. However, such equilibrium state usually cannot be captured by numerical methods due to discretization errors. Consequently, inconsistent thermodynamic interfacial properties due to non-constant chemical potential, and spurious velocities due to discrete force imbalance, are frequently encountered in numerical simulations. Therefore, numerical schemes with well-balanced properties, which can capture the equilibrium state at discrete level, are preferred for simulating two-phase flows. In this paper, we report the progress of developing well-balanced mesoscopic numerical methods based on kinetic theory, focusing on the lattice Boltzmann equation (LBE) method and the discrete unified gas-kinetic scheme (DUGKS). First, the discrete balance property of a free-energy LBE for single-component two-phase flows is analyzed to identify the structure of force imbalance. Then, a well-balanced LBE (WB-LBE) model which has the same algorithm structure as the standard one is reviewed. The WB-LBE is theoretically shown to be able to achieve the discrete equilibrium state, and the well-balance properties are confirmed numerically. Some extensions to other two-phase LBE models are discussed with enhanced numerical stability. The well-balanced DUGKS, which can use non-uniform meshes and exhibits better numerical stability for large density ratio systems is also reported. • The WB-LBE reaches discrete equilibrium state both theoretically and numerically. • The WB-LBE has ability to deal with wetting boundary conditions well. • Extended WB-LBE models with enhanced numerical stability are reviewed. • The WB-DUGKS which shows well-balanced property is reviewed. [ABSTRACT FROM AUTHOR]

In this paper, we develop the explicit second derivative multistep methods (SDMMs) for the Euler and Navier–Stokes equations. The SDMMs use the calculated results from the previous steps, which can improve computational efficiency. The third-order and fourth-order SDMMs temporal discretization methods are constructed based on the order conditions. Additionally, the strong stability preserving (SSP) condition for the SDMMs is proposed, which provides the corresponding parameters for optimal SSP SDMMs. For numerical experiments, the SDMMs can achieve the order of accuracy as designed on the smooth regions, and the optimal SSP coefficient for the SDMMs is shown to be roughly the same in theory as in the numerical results. Moreover, the SDMMs have approximately twice the computational efficiency compared with the third-order and fourth-order two-derivative Runge–Kutta methods, and the SDMMs are also more efficient than the classical three-stage third-order SSP Runge–Kutta method. • The strong stability preserving theory of explicit SDMMs are developed. • The third-order and fourth-order SDMMs with the optimal SSP coefficient are proposed. • The explicit SDMMs are utilized to calculate the Euler and Navier–Stokes equations. • The SDMMs demonstrate a superior improvement in computational efficiency compared to the Runge–Kutta methods. [ABSTRACT FROM AUTHOR]

The sharp interface immersed boundary method (IBM) is a powerful tool to simulate the flow around moving objects. This paper extends this method to simulate the motion of particles immersed in a fluid. We introduce a new implicit coupling scheme between the solid and fluid phases, verify the high–order of convergence of the scheme, and validate it using four cases. The fluid dynamics is simulated using a streamline upwind Petrov–Galerkin and pressure-stabilizing Petrov–Galerkin (SUPG/PSPG) stabilizations. The particles' dynamics and contact are solved using Newton's second law of motion and a soft sphere contact model derived from the discrete element method. The first validation case is the sedimentation of a lone particle with a Reynolds number smaller than 32. The second validation case is the rise of a positively buoyant particle at a high Reynolds number (2500). The third validation case demonstrates the stability of the scheme when particles are in contact and exhibit the classical drafting, kissing, and tumbling (DKT) behavior. Finally, we use the scheme to study the Boycott effect with a larger number of particles (64) to show the stability of the scheme in cases with numerous particle–particle and particle–wall contacts. • A Resolved CFD-DEM scheme using high–order sharp interface immersed boundary method. • An implicit coupling scheme stable for low particle–to–fluid density ratio. • A 3D verification case that demonstrates the high–order of convergence of the scheme. • Four validation cases with varying complexity covering Reynolds number 1 to 2500. [ABSTRACT FROM AUTHOR]

• A strongly conservative solver for cylindrical coordinates is proposed. • The analytical solution of the uniform flow is numerically obtained in the cylindrical coordinates. • The singularity of the cylindrical coordinates at the pole is addressed. • The time step constrained around the z-axis is significantly improved. • A strongly conservative methodology is proposed for curvilinear coordinates. Cylindrical coordinates are often used in computational fluid dynamics (CFD), particularly when one considers axisymmetric flow. Although cylindrical coordinates have several advantages in accurately describing the rotational flow as well as the complex boundary, there are limits to how far they can be taken. These are (1) the governing equations are mostly in a non-conservative form in current standard models, which cannot preserve the conservation of numerical simulations, (2) the singularity along the axis at the coordinate origin (z -axis), leading to difficulty reproducing the flow across the z -axis, and (3) the time step is extremely shortened to satisfy the CFL condition near the z -axis because the numerical cell thereof is narrow in the azimuthal direction for a given angular resolution. A strongly conservative model is proposed in this paper to overcome these difficulties. First, the strongly conservative form of the governing equations is derived by considering changes in the direction of the base vector within a cell, and a concept of direction error is defined to reveal the inherent error of the standard model. Second, inspired by the derivation of the first, a strongly conservative method for evaluating the flux across each cell surface is proposed, preserving the conservation of discretization and enlarging the time step. Finally, the proposed model is tested by three classical problems, i.e., uniform flow, Sod shock tube problem, and expanding outflows. The results imply that the proposed model is strongly conservative for the cylindrical coordinate system, and it can overcome the limits of the standard model and eliminate the inherent error in the standard model. Furthermore, the strongly conservative model and method are extended to arbitrary coordinates for the numerical conservation in general curvilinear coordinates of the problem with complex boundaries. [ABSTRACT FROM AUTHOR]