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In this paper, we introduce a hybrid LBM-FVM solver for two-phase fluid flow simulations in which interface dynamics is modeled by a conservative phase-field equation. Integrating fluid equations over time is achieved through a velocity-based lattice Boltzmann solver which is improved by a central-moment multiple-relaxation-time collision model to reach higher accuracy. For interface evolution, we propose a finite-volume-based numerical treatment for the integration of the phase-field equation: we show that the second-order isotropic centered stencils for diffusive and separation fluxes combined with the WENO-5 stencils for advective fluxes achieve similar and sometimes even higher accuracy than the state-of-the-art double-distribution-function LBM methods as well as the DUGKS-based method, while requiring less computations and a smaller amount of memory. Benchmark tests (such as the 2D diagonal translation of a circular interface), along with quantitative evaluations on more complex tests (such as the rising bubble and Rayleigh-Taylor instability simulations) allowing comparisons with prior numerical methods and/or experimental data, are presented to validate the advantage of our hybrid solver. Moreover, 3D simulations (including a dam break simulation) are also compared to the time-lapse photography of physical experiments in order to allow for more qualitative evaluations. • This paper proposes a new hybrid LBM-FVM solver to simulate two-phase flows which reduces memory consumption and improves computational accuracy and efficiency. • The momentum equation is solved by a set of lattice Boltzmann equations with a velocity-based high-order CM-MRT model, while the phase-field equation is solved by a WENO-based finite-volume approach. • Our solver is validated through benchmark tests, comparisons, and validation examples, both quantitatively and qualitatively. • Our massively-parallel implementation on GPU offers efficient simulation of two-phase flows for a low memory footprint. [ABSTRACT FROM AUTHOR]

Robust iterative methods for solving large sparse systems of linear algebraic equations often suffer from the problem of optimizing the corresponding tuning parameters. To improve the performance of the problem of interest, specific parameter tuning is required, which in practice can be a time-consuming and tedious task. This paper proposes an optimization algorithm for tuning the numerical method parameters. The algorithm combines the evolution strategy with the pre-trained neural network used to filter the individuals when constructing the new generation. The proposed coupling of two optimization approaches allows to integrate the adaptivity properties of the evolution strategy with a priori knowledge realized by the neural network. The use of the neural network as a preliminary filter allows for significant weakening of the prediction accuracy requirements and reusing the pre-trained network with a wide range of linear systems. The detailed algorithm efficiency evaluation is performed for a set of model linear systems, including the ones from the SuiteSparse Matrix Collection and the systems from the turbulent flow simulations. The obtained results show that the pre-trained neural network can be effectively reused to optimize parameters for various linear systems, and a significant speedup in the calculations can be achieved at the cost of about 100 trial solves. The hybrid evolution strategy decreases the calculation time by more than 6 times for the black box matrices from the SuiteSparse Matrix Collection and by a factor of 1.4–2 for the sequence of linear systems when modeling turbulent flows. This results in a speedup of up to 1.8 times for the turbulent flow simulations performed in the paper. • A hybrid evolution strategy for optimizing the parameters of linear solvers is proposed. • The pre-trained neural network used as a pre-filter allows for improving the quality of optimization. • The pre-trained neural networks can be reused to optimize a variety of linear systems across different compute platforms. • Optimizing the parameters of linear solvers allows for the acceleration of incompressible turbulent flow simulations. [ABSTRACT FROM AUTHOR]

Fluid-solid interaction (FSI) phenomena play an important role in many biomedical engineering applications. While FSI techniques and models have enabled detailed computational simulations of flow and tissue motion, the application of FSI can present challenges, particularly when data for constraining models is sparse and/or when fast computational simulations are required for assessment. In this paper, we propose a novel method for flexible-wall fluid dynamics in an ALE framework applicable for cardiovascular applications where adaptive fluid motion that emulates patient data is required. Efficiency and model simplicity are gained by a physics-based reduction to solid membrane formulations at the fluid-tissue interface combined with a Galerkin projection to a subspace spanned by boundary motion modes, leveraging snapshots observed from imaging data by use of Proper Orthogonal Decomposition (POD). The resulting fluid-reduced-solid interaction (FrSI) model is verified for a series of examples, illustrating efficacy and efficiency. Focusing on an idealized left ventricle model, we demonstrate homogenization of transmural active stress along with the capacity to accommodate prestress in the FrSI model, accounting for whole cycle mechanics by coupling to 0D pre- and afterload models (showing end-diastolic and end-systolic projected endocardial surface position errors of less than 1.5% and 3.5%, respectively). Further, we present strategies to compensate for the inherent approximation errors of the FrSI model, allowing for minimizing both the integral and spatial error between reduced and full-order model by re-calibrating parameters that govern diastolic and systolic function. Finally, the ability of FrSI to extrapolate to impaired system states (increased afterload, localized region of infarct) is shown, providing a simple yet effective strategy to enhance the POD subspace to further reduce errors. These results illustrate the potential of FrSI to streamline the simulation of hemodynamics in the heart and cardiovascular system. • Novel model reduction for cardiovascular fluid-solid interaction (FSI). • Physics- and projection-based approach to address the solid mechanics problem in FSI. • Suitable for modeling large-deformation mechanics using 'fluid-only' discretization. • Full-cycle ventricular mechanics with low spatial and integral errors. • Efficient approach to streamline hemodynamics simulations in the heart and arteries. [ABSTRACT FROM AUTHOR]

The present paper focuses on lattice Boltzmann method (LBM) simulations of turbulent flows in combination with a Zonal Detached Eddy Simulation (ZDES) approach, specifically its mode 2 (2020). A common issue of the concomitant use of LBM and DES type models is the systematic modeled-stressed depletion (MSD) triggered by fine isotropic grids imposed by the lattice. This issue is responsible for erroneous surface coefficients that can eventually lead to grid induced separation (GIS). In this work, it is shown that the enhanced boundary layer protection brought by ZDES mode 2 (2020) is sufficient to allow the combination of LBM and a DES type method for high Reynolds number with equal accuracy as its Navier-Stokes counterpart. The emphasis is put on the ability of ZDES to recover its main properties within the numerics of lattice Boltzmann formalism. This is achieved on multiple test-cases namely the turbulent flow over a flat plate, a backward facing step and a three-element airfoil. • Salient combination of lattice Boltzmann Method and Zonal Detached Eddy Simulation. • RANS shielding of turbulent boundary layers ensured even on fine LBM-induced grids. • Consistency between the model and its Navier-Stokes counterpart. • Model assessment on flat plate, backward-facing step and three-element airfoil test-cases. • Robust combination promising for industrial applications. [ABSTRACT FROM AUTHOR]

This paper presents a novel projection-based embedded discrete fracture model (pEDFM) applicable to general two-phase flow simulation in anisotropic reservoirs for the first time. The novel pEDFM is developed based on hybrid two-point flux approximation and mimetic finite difference (TPFA-MFD) methods, which retains the basic features of two-point flux approximation (TPFA) based generic pEDFM workflow and incorporates new features of mimetic finite difference (MFD) to handle full-tensor permeabilities. This is achieved by introducing the concept of effective connection, formulating additional pressure degrees of freedom for effective connections, assigning effective matrix-matrix (m-m) and matrix-fracture (m-f) connections to the corresponding sides of matrix-cell interfaces, presenting methods corresponding to different types of connections to handle low-conductivity fractures, and further deriving formulas of numerical fluxes for effective connections. The resulting global equation system is solved by a Newton-Raphson nonlinear solver with the temporary discretization of the implicit backward Euler scheme. The 2D and 2.5D numerical examples show the novel pEDFM could achieve the same level of computation accuracy and convergence as the reference discrete fracture model (DFM), while avoiding the gridding difficulty of complex fracture networks. It also significantly outperforms classical EDFM based on MFD and generic pEDFM workflow in the computational accuracy for cases with anisotropic full tensor permeabilities. The novel pEDFM, to our best knowledge, is for the first time proposed and developed for general anisotropic two-phase flow simulation and maybe the numerical simulation framework for multi-phase flow in fractured reservoirs with the best comprehensive performance so far. [ABSTRACT FROM AUTHOR]

This paper presents under-resolved simulations of compressible flows in complex structures like buildings. The mean pressure field is the primary focus as it is of high importance in many cases, such as the overpressure generated by the detonation of an explosive charge. In such high-risk situations, the mean pressure in the different building rooms has to be determined as quickly as possible, in order to help first responders evaluating the risk level of entering the building right after an explosion for instance. Conventional computational fluid dynamics methods are obviously able to deliver those requested pressure fields. However, they also require a long and tedious meshing process due to the presence of small openings in the computational domain (doors, windows or stairwells). In turn, these small openings need spatial and temporal resolution having significant consequences on computation time. But when dealing with pressing situations, a long pre-processing is not acceptable. The present paper proposes a two-step solution method. First, a very rough mesh is constructed which does not consider small openings. The mesh is constructed in an easy and particular way such that simplifications can be made when computing the fluid flux through these openings. Second, a specific Riemann solver dealing with geometric discontinuities is developed to estimate the fluid flow. The Riemann solver takes advantage of the simplifications provided by the meshing method, and accounts for both unchoked and choked flows through openings. The overall method then consists of both a specific meshing process that requires very little pre-processing, which considerably reduces the time needed to produce a complete simulation, and a Riemann solver. The proposed method is named MUZO in reference to its "MUlti-ZOne" flow solver. The MUZO solver is validated against resolved computations and provides accurate simulated mean pressure fields within a realistic building in a few seconds. • 3D simulations of compressible flow discharge in buildings are addressed through a very fast numerical framework. • Only 2D footprints without geometric details (doors, windows, etc.) are required to generate 3D meshes. • The previously omitted geometric restrictions are considered through a specific Riemann solver. [ABSTRACT FROM AUTHOR]

As the number of processors on supercomputers has increased dramatically, there is a growing interest in developing scalable algorithms with a high degree of parallelism for extreme-scale reservoir simulation. However, traditional simulators and algorithms for such nonlinear problems are usually based on the family of time-marching methods, where parallelization is restricted to the spatial dimension only. In this paper, we propose a family of parallel-in-time (PinT) reservoir algorithms for solving multiphase flow problems in porous media to fully exploit the parallelism of supercomputers, in which the design of efficient nonlinear and linear space-time algorithms plays an essential role. More precisely, we first introduce a space-time mixed finite element method for the fully-implicit discretization. The nonlinear system arising at each parallel-in-time step is solved by a variant of bound-preserving Newton methods with a nonlinear elimination preconditioner, where the corresponding linear system is solved by the space-time restricted additive Schwarz (stRAS) method. Since the straightforward extension of one-level stRAS to multilevel does not work because of the pollution effects from the temporal direction, we accordingly present a nonstandard V-cycle multilevel stRAS method with a pollution-removing strategy to accelerate the convergence and improve the robustness. Numerical experiments are presented to demonstrate that the aforementioned parallel-in-time algorithm can not only achieve a high degree of parallelism in accurately resolving reservoir transport features in a heterogeneous medium, but also successfully circumvent the convergence and scalability issues associated with the constraint of large time steps and the boundedness requirement of the solution. • Space-time mixed finite element scheme for parallel in-time discretization. • Active-set reduced-space method with nonlinear elimination for bound-preserving solution. • Space-time restricted additive Schwarz algorithm for linear preconditioning. • Nonlinear parallel-in-time simulations with up to 13,872 processor cores. [ABSTRACT FROM AUTHOR]

When solving compressible multi-material flow problems, an unresolved challenge is the computation of advective fluxes across material interfaces that separate drastically different thermodynamic states and relations. A popular idea in this regard is to locally construct bimaterial Riemann problems, and to apply their exact solutions in flux computation. For general equations of state, however, finding the exact solution of a Riemann problem is expensive as it requires nested loops. Multiplied by the large number of Riemann problems constructed during a simulation, the computational cost often becomes prohibitive. The work presented in this paper aims to accelerate the solution of bimaterial Riemann problems without introducing approximations or offline precomputation tasks. The basic idea is to exploit some special properties of the Riemann problem equations, and to recycle previous solutions as much as possible. Following this idea, four acceleration methods are developed, including (1) a change of integration variable through rarefaction fans, (2) storing and reusing integration trajectory data, (3) step size adaptation, and (4) constructing an R-tree on the fly to generate initial guesses. The performance of these acceleration methods is assessed using four example problems in underwater explosion, laser-induced cavitation, and hypervelocity impact. These problems exhibit strong shock waves, large interface deformation, contact of multiple (>2) interfaces, and interaction between gases and condensed matters. For all the problems, the acceleration methods are able to significantly reduce the computational cost without affecting solver robustness or solution accuracy. In different cases, the solution of bimaterial Riemann problems is accelerated by 37 to 87 times. As a result, the total cost of advective flux computation, which includes the exact Riemann problem solution at material interfaces and the numerical flux calculation over the entire computational domain, is accelerated by 18 to 81 times. • Bimaterial Riemann problems can be constructed to compute interfacial fluxes. • Computational cost is often prohibitive, if complex equations of state are involved. • An efficient exact Riemann solver is proposed, with four algorithmic improvements. • Significant cost reduction (37-87X) is achieved for four challenging examples. • Does not introduce approximations or require offline precomputation. [ABSTRACT FROM AUTHOR]

In this paper, we mainly concern with the order reduction for the unknown solution coefficient vectors about the classical continuous space-time finite element (CCSTFE) method of the two-dimensional (2D) non-stationary incompressible Navier-Stokes equations. Therefore, we first build the CCSTFE scheme for the 2D non-stationary Navier-Stokes equations with respect to stream–vorticity functions, give the existence and stability together with convergence to the CCSTFE solutions, and rewrite the CCSTFE scheme as a matrix form. And then, we use a proper orthogonal decomposition (POD) technique to build a reduced-order extrapolated continuous space-time finite element (ROECSTFE) scheme in the matrix form including very few unknowns but possessing high enough accuracy, employ matrix analysis to demonstrate the existence and stability together with convergence of the ROECSTFE solutions such that the theoretical analysis becomes very concise and convenient, and summarize the flowchart for solving the ROECSTFE scheme. Finally, we take advantage of the numerical simulations for the back-step flow and the flow around airfoil problem to verify the correctness of theoretical results. • The continuous space-time finite element (CSTFE) method for unsteady Navier-Stokes equations is proposed for the first time. • The reduced-order extrapolated CSTFE scheme is established in this paper for the first time. • Using matrix tool to argue the existence, stability, convergence of the numerical solutions leads to very laconic theoretic analysis. • The back-step flow and the flow around airfoil problem are simulated. [ABSTRACT FROM AUTHOR]

A generalized coupled level set/volume-of-fluid/ghost fluid method for the detailed simulation of gas-liquid flows is proposed in this paper. The interface is captured by the coupled level set and volume-of-fluid method, where the level set method is used to compute normal vector and curvature accurately, and the volume-of-fluid method is used to conserve the global volume or mass. The ghost fluid method is also used for discretization across the interface. The novelty of the present approach lies in that a generalized formulation for the conversion between the level set function and the volume-of-fluid function is proposed in a simple and efficient manner. Three benchmarks, including Zalesak's disk, two-dimensional deformation and three-dimensional deformation, are used for validation and verification. It shows that excellent agreement is achieved, and the present method has first-order accuracy. The current method is further applied to the simulations of droplet dynamics, rising bubbles, head-on droplet collision and liquid jet breakup, demonstrating the capability to accurately capture the interface. • A generalized coupled level set/volume-of-fluid/ghost fluid method for detailed simulation of gas-liquid flows is proposed. • The present work utilizes level set method and volume-of-fluid method to capture the interface. • A generalized formulation for the conversion is proposed in a simple and efficient manner. • The present framework has been validated by several cases. • The coupling procedure is easy to be implemented in the existing interface capturing method. [ABSTRACT FROM AUTHOR]

This paper presents a strategy to accelerate virtually any Poisson solver by taking advantage of s spatial reflection symmetries. More precisely, we have proved the existence of an inexpensive block diagonalisation that transforms the original Poisson equation into a set of 2 s fully decoupled subsystems then solved concurrently. This block diagonalisation is identical regardless of the mesh connectivity (structured or unstructured) and the geometric complexity of the problem, therefore applying to a wide range of academic and industrial configurations. In fact, it simplifies the task of discretising complex geometries since it only requires meshing a portion of the domain that is then mirrored implicitly by the symmetries' hyperplanes. Thus, the resulting meshes naturally inherit the exploited symmetries, and their memory footprint becomes 2 s times smaller. Thanks to the subsystems' better spectral properties, iterative solvers converge significantly faster. Additionally, imposing an adequate grid points' ordering allows reducing the operators' footprint and replacing the standard sparse matrix-vector products with the sparse matrix-matrix product, a higher arithmetic intensity kernel. As a result, matrix multiplications are accelerated, and massive simulations become more affordable. Finally, we include numerical experiments based on a turbulent flow simulation and making state-of-the-art solvers exploit a varying number of symmetries. On the one hand, algebraic multigrid and preconditioned Krylov subspace methods require up to 23% and 72% fewer iterations, resulting in up to 1.7x and 5.6x overall speedups, respectively. On the other, sparse direct solvers' memory footprint, setup and solution costs are reduced by up to 48%, 58% and 46%, respectively. • Exploiting symmetries simplifies meshing complex geometries. • The overhead of the two (communication-free) transforms is negligible. • Iterative solvers converge much faster by making Poisson's equation block diagonal. • SpMM reduces the memory footprint of the matrices and accelerates their multiplications. • Extreme-scale simulations become considerably more affordable. [ABSTRACT FROM AUTHOR]

The paper is concerned with an adjoint complement to the Volume-of-Fluid (VoF) method for immiscible two-phase flows, e.g. air and water, which is widely used in marine engineering due to its computational efficiency. The particular challenge of the primal and the corresponding adjoint VoF-approach refers to the sharp interface treatment featuring discontinuous physical properties. Both the continuous adjoint two-phase system (integration-by-parts) and the corresponding dual compressive convection schemes (summation-by-parts) are derived for two prominent compressive convection schemes, namely the High Resolution Interface Capturing Scheme (HRIC) and Compressive Interface Capturing Scheme for Arbitrary Meshes (CICSAM). The dual scheme rigorously mirrors the primal Normalized-Variable-Diagram (NVD) stencils. Attention is restricted to steady state applications. Thus both the primal and the dual procedures are performed in pseudo-time and the backward integration of the dual approach is performed around the (pseudo-temporal) converged primal field. Therefore, the adjoint system experiences the same time step size restrictions as the primal system, is independent of the primal time horizon and forms a robust as well as an a priori stable adjoint solution process. The paper analyses the primal and adjoint equations for an engineering model problem. An analytical solution to the model problem is initially presented, which displays that the adjoint part does not offer a unique, non-trivial solution. As a remedy, an additional diffusive concentration term is introduced to the adjoint concentration equation. The imposed heuristic modification violates the dual consistency but strongly regularizes the solution of the adjoint system. The modification can be justified by reference to phase-separating diffuse-interface models and inheres a free mobility-parameter. Numerical results obtained from the modified approach are benchmarked against the analytical solution for the model problem. Supplementary, the influence of the modification on the sensitivities obtained from simulations for the two-dimensional flow around a submerged hydrofoil at Froude and Reynolds numbers of practical interest are discussed for a range of mobility-parameters. The final application refers to a shape-optimization of a generic 3D underwater vehicle and underlines a negligible influence of the free mobility parameter, even for an objective functional that directly depends on the manipulated (dual) field quantity. • Hybrid (continuous and discrete) derivation of the adjoint Volume-of-Fluid equation. • Adjoint High Resolution Interface Capturing Scheme. • Adjoint Compressive Interface Capturing Scheme for Arbitrary Meshes. • Primal/Dual sub-cycling procedure allows for an efficient pseudo-time stepping. • Full Derivative of the material-law outperforms a frozen-material-law approach. [ABSTRACT FROM AUTHOR]

A generic balanced-force algorithm is proposed to solve incompressible multiphase flows with complex interfaces and large density ratios on the polyhedral unstructured grids of large non-orthogonality, skewness and non-uniformity. This algorithm combines the finite volume method based on the volume of fluid (VOF) approach with the fractional step method in a collocated framework, which retains a complete balance between the gravity, surface tension with exact curvature, and the resulting pressure gradients. In the original scheme, the gravity and surface tension terms are represented as gradients of the volume fraction and then discretized in the identical fashion as the pressure gradient, which results in a balanced formulation on the structured grids. However, this scheme cannot be readily applied to unstructured grids, despite that it has been misused for more than one decade. As demonstrated in the paper, it is insufficient to achieve force balance merely by the identical discretization of scalar gradients due to the non-orthogonality of unstructured grids, which will generate severe spurious currents that intensify with larger non-orthogonality angle and higher fluid density ratio. Therefore, we present a novel balanced-force algorithm to treat the non-orthogonal term in a different manner, which significantly suppresses, or even eliminates, the spurious velocity for two-phase flows with large density ratio on arbitrary mesh topology. Various numerical examples have demonstrated that the present algorithm and computational framework offer a promising platform to provide high-fidelity and robust predictions for practical multiphase flow simulations involving highly complex geometry. • Balanced-force algorithm for multiphase flows with large density ratios and distorted grids. • Machine precision of spurious currents on unstructured grids with large non-orthogonality. • Equilibrium solution and rapid convergence for the semi-implicit pressure Poisson equation. • High-fidelity simulation for practical multiphase flow problems involving complex geometry. [ABSTRACT FROM AUTHOR]

This paper develops a tree-topological local mesh refinement (TLMR) method on Cartesian grids for the simulation of bio-inspired flow with multiple moving objects. The TLMR nests refinement mesh blocks of structured grids to the target regions and arrange the blocks in a tree topology. The method solves the time-dependent incompressible flow using a fractional-step method and discretizes the Navier-Stokes equation using a finite-difference formulation with an immersed boundary method to resolve the complex boundaries. When iteratively solving the discretized equations across the coarse and fine TLMR blocks, for better accuracy and faster convergence, the momentum equation is solved on all blocks simultaneously, while the Poisson equation is solved recursively from the coarsest block to the finest ones. When the refined blocks of the same block are connected, the parallel Schwarz method is used to iteratively solve both the momentum and Poisson equations. Convergence studies show that the algorithm is second-order accurate in space for both velocity and pressure, and the developed mesh refinement technique is benchmarked and demonstrated by several canonical flow problems. The TLMR enables a fast solution to an incompressible flow problem with complex boundaries or multiple moving objects. Various bio-inspired flows of multiple moving objects show that the solver can save over 80% computational time, proportional to the grid reduction when refinement is applied. • We develop a Cartesian-grid-based mesh refinement method for solving incompressible Navier-Stokes equations. • The method uses tree-topological mesh refinement blocks wherever high-resolution meshes are needed around immersed bodies. • We solve a set of two- and three-dimensional canonical flows to establish the accuracy and fidelity of the method. • We study the computation efficiency of the solver using highly complicated biofluid problems with multiple moving objects. [ABSTRACT FROM AUTHOR]

Computational fluid dynamics is a direct modeling of physical laws in a discretized space. The basic physical laws include the mass, momentum and energy conservations, numerical scale-consistent transport process, and similar domain of dependence and influence in the physical and the numerical wave propagations. Therefore, a physically soundable numerical scheme should be a compact one which involves the closest neighboring cells within the domain of dependence for the solution update under a CFL number (∼1). In order to keep the compactness of the scheme and be high-order, subcell flow distributions or the equivalent degrees of freedom beyond the cell averaged flow variables are needed, such as the gradients of the flow variables inside each control volume. Under the above consideration, the direct use of Riemann solver as the evolution model doesn't provide such a mechanism. High-order dynamic evolution process should be used to update the time accurate cell-averaged flow variables and their gradients. The direct modeling of flow evolution under generalized initial condition will be developed. In order to provide reliable cell averaged flow variables and their gradients for the compact data reconstruction, the evolution process is constructed to provide possible discontinuous time-dependent flow variables across a cell interface. At the same time, the time accurate flux function at a cell interface can become a discontinuous function of time in its evolution process. Same as the spatial limiter in the conventional computational fluid dynamics methods, such as the total variation diminishing and weighted essentially non-oscillatory methods, the temporal limiter for the time accurate flux function is designed as well. The direct modeling method in this paper will update flow variables differently on both sides of a cell interface and nonlinearly limit the high-order time derivatives of the flux function in case of shock wave passing through a cell interface within a time step. The direct modeling method unifies the concepts of nonlinear limiters in spatial data reconstruction and temporal flux transport. The equivalent treatment of space and time makes the compact gas-kinetic scheme be super robust and accurate for the compressible flow simulation. At the same time, the 4th to 8th-order compact schemes can use a large CFL number (∼ 0.8) in flow computation, even for the hypersonic flow simulation. • A general principle for the development of high-order compact scheme is presented. • Same as the nonlinear limiter in space, the nonlinear limiter in time for the flux function is proposed. • According to the principle the high-order compact gas-kinetic scheme is developed. • Accurate solutions of compressible Euler and Navier-Stokes equations are obtained. [ABSTRACT FROM AUTHOR]

The asynchronous computing method based on finite-difference schemes has shown promise in significantly improving the scalability of time-dependent partial differential equation (PDE) solvers by either relaxing data synchronization or avoiding communication between processing elements (PEs) on massively parallel machines. This method uses high-order accurate asynchrony-tolerant (AT) schemes coupled with appropriate time integration schemes to provide the desired accuracy required by high-fidelity solvers such as the direct numerical simulations for fluid flow. For time integration, Runge-Kutta (RK) schemes, particularly the low-storage implementation, are widely used due to their ability to provide good stability properties and be computationally efficient. However, the implementation of AT schemes with multi-stage RK schemes necessitates an over-decomposition of the spatial domain in a parallel setting, leading to increased message sizes for communication and redundant computations. In this paper, we propose a novel method to couple asynchrony-tolerant and low-storage explicit RK schemes in solving time-dependent PDEs that would result in a significant reduction in communications and relaxed synchronizations. We develop new asynchrony-tolerant schemes for ghost or buffer point updates that are necessary to maintain desired order of accuracy. The accuracy of this method is investigated, both theoretically and numerically, using simple one-dimensional linear model equations. Thereafter, we demonstrate the scalability of the proposed numerical method through three-dimensional simulations of decaying Burgers' turbulence, performed using two different asynchronous algorithms: communication-avoiding and synchronization-avoiding algorithms. The scalability studies up to 27 , 000 cores were found to yield speed-ups up to 6× compared to a baseline synchronous algorithm. Overall, the proposed approach shows the potential to improve the scalability of exascale PDE solvers significantly. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel approximation strategy for time-dependent hyperbolic systems of conservation laws for the Euler system of gas dynamics that aims to represent the dynamics of strong interacting discontinuities. The goal of our method is to allow an approximation with a high-order of accuracy in smooth regions of the flow, while ensuring robustness and a non-oscillatory behaviour in the regions of steep gradients, in particular across shocks. Following the Multidimensional Optimal Order Detection (MOOD) ([15,17]) approach, a candidate solution is computed at a next time level via a high-order accurate explicit scheme ([3,5]). A so-called detector determines if the candidate solution reveals any spurious oscillations or numerical issue and, if so, only the troubled cells are locally recomputed via a more dissipative scheme. This allows to design a family of "a posteriori" limited, robust and positivity preserving, as well as high accurate, non-oscillatory and effective scheme. Among the detecting criteria of the novel MOOD strategy, two different approaches from literature, based on the work of [15,17] and on [35] , are investigated. Numerical examples in 1D and 2D, on structured and unstructured meshes, are proposed to assess the effective order of accuracy for smooth flows, the non-oscillatory behaviour on shocked flows, the robustness and positivity preservation on more extreme flows. • Presentation of a novel MOOD strategy for multidimensions. • MOOD on high order Residual Distribution schemes for compressible flows. • Application of the strategy to triangle and quad meshes. [ABSTRACT FROM AUTHOR]

We present rotating periodic boundary conditions (PBCs) for the simulation of nonequilibrium molecular dynamics (NEMD) under uniaxial stretching flow (USF) or biaxial stretching flow (BSF). Such nonequilibrium flows need specialized PBCs since the simulation box deforms with the background flow. The technique builds on previous models using one or two lattice remappings, and is simpler than the PBCs developed for the general three dimensional flow. For general three dimensional flows, Dobson [1] and Hunt [2] proposed schemes which are not time-periodic since they use more than one automorphism remapping. This paper presents a single automorphism remapping PBCs for USF and BSF which is time periodic up to a rotation matrix and has better minimum lattice spacing properties. • Handles deforming simulation domains for uniaxial flows using a single remapping. • Long-time stable simulation which is periodic up to a rotation. • The scheme cannot be made time periodic in a large remapping class. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel discrete fracture model for flow simulation of fractured porous media containing flow blocking barriers on non-conforming meshes. The methodology of the approach is to modify the traditional Darcy's law into the hybrid-dimensional Darcy's law where fractures and barriers are represented as Dirac- δ functions contained in the permeability tensor and resistance tensor, respectively. As a natural extension of the previous discrete fracture model [21] for highly conductive fractures, this model is able to account for the influence of both highly conductive fractures and blocking barriers accurately on non-conforming meshes. The local discontinuous Galerkin (LDG) method is employed to accommodate the form of the hybrid-dimensional Darcy's law and the nature of the pressure/flux discontinuity. The performance of the model is demonstrated by several numerical tests. • Introduce line Dirac delta functions into the discrete fracture model for fracture and barrier networks. • Construct discontinuous Galerkin methods for the discrete fracture model on noncon- forming meshes. • Apply the model to steady state single phase flow and contaminant transportation in fractured porous media. [ABSTRACT FROM AUTHOR]

In this paper we propose a primal C 0 -conforming virtual element discretization for the simulation of the two-phase flow of immiscible fluids in poro-fractured media modeled by means of a Discrete Fracture Network (DFN). The fractures are assumed to be made of the same isotropic rock type and to have the same width. The flexibility of the Virtual Element Method (VEM) in handling general polygonal elements allows to obtain a global conformity of the DFN mesh while preserving a fracture-independent meshing approach. The effectiveness and the robustness of the proposed numerical method are tested on DFN configurations of increasing complexity and characterized by challenging mesh geometry. • Use of non-standard polygonal conforming meshes on complex Discrete Fracture Network (DFN). • Primal conforming Virtual Element Method (VEM) approach for immiscible two-phase flow in poro-fractured media. • Solution of complex non-linear problems on challenging mesh geometries. [ABSTRACT FROM AUTHOR]

• Consistent phase-change procedure are proposed and investigated for any interface capturing method. • Accurate and second-order discretizations for diffusion operator with flux jump are presented. • Second-order accurate gradients from any interface representation are obtained. • VOF and Level-Set framework for evaporating flows are limited to first-order convergence with important errors in 3D. In this paper, the modeling of phase change in an incompressible two-phase flow solver is detailed without restricting the numerical methods to a specific interface capturing method. Starting from existing methodologies of the literature, the present work gives a step-by-step investigation of each numerical aspect of phase change to obtain an accurate and consistent solver. The main challenge when including phase-change is the handling of flux discontinuities at the interface when advancing temperature and species mass fraction. An accurate and second order discretization is proposed for any Eulerian representation of the interface either by adding a sharp source term or by imposing a boundary condition at the interface. As the accuracy and convergence rate of such solver are driven by the reconstruction of the evaporation rate m ˙ , particular attention is devoted to the reconstruction of gradient normal to the interface. Several methodologies are proposed to compute second-order gradients at the interface location adapted to any interface representation. Applying such techniques to a second-order accurate field leads to an expected first order accuracy of m ˙ but with remarkable accuracy improvements using ghost cell methods with quadratic extrapolation. Then, several phase-change procedures are built by combining a selection of numerical methods to handle flux discontinuities and evaluate gradients. The procedures are investigated on planar phase-change simulations to bring out inconsistent combination choices. Finally, a multidimensional evaporation test case is presented to show the final accuracy and limitations of phase-change modeling in today two-phase flow solvers. [ABSTRACT FROM AUTHOR]

In this paper, we construct a combined multiscale finite element method (MsFEM) using the Local Orthogonal Decomposition (LOD) technique to solve the multiscale problems which may have singularities in some special portions of the computational domain. For example, in the simulation of steady flow transporting through highly heterogeneous porous media driven by extraction wells, the singularities lie in the near-well regions. The basic idea of the combined method is to utilize the traditional finite element method (FEM) directly on a fine mesh of the problematic part of the domain and using the LOD-based MsFEM on a coarse mesh of the other part. The key point is how to define local correctors for the basis functions of the elements near the coarse and fine mesh interface, which require meticulous treatment. The proposed method takes advantages of the traditional FEM and the LOD-based MsFEM, which uses much less DOFs than the standard FEM and may be more accurate than the LOD-based MsFEM for problems with singularities. The error analysis is carried out for highly varying coefficients, without any assumptions on scale separation or periodicity. Numerical examples with periodic and random highly oscillating coefficients, as well as the multiscale problems on the L-shaped domain, and multiscale problems with high-contrast channels or well-singularities are presented to demonstrate the efficiency and accuracy of the proposed method. • A combined MsFEM is proposed to solve the multiscale problem with singularities. • A special definition of the local correctors for the interface-elements is given. • The error analysis is carried out for arbitrary varying coefficients. • Error estimates are independent of the ratio of the coarse-fine mesh sizes. • The method is very efficient for multiscale problems with well-singularities. [ABSTRACT FROM AUTHOR]

The highly nonlinear nature of the system governing equations makes it difficult to simulate viscoelastic flows efficiently. In this paper, an implicit decoupling approach is proposed for the viscoelastic flow simulation with a monolithic projection method. The decoupling approach can be derived from the approximate block factorization at the matrix level, which has been successfully applied into the Newtonian flow simulations. In our work, we extend this approach to decouple the pressure, conformation tensor and velocity from the viscoelastic flow system sequentially. Firstly, the pressure-conformation tensor-velocity decoupling is realized by a two-step approximate factorization. By combining the conformation tensor and velocity together at the first-step factorization, the original efficient pressure Poisson solver for the Newtonian flow simulation can be directly adopted in the present framework for non-Newtonian flow simulation. Secondly, the conformation tensor components are further decoupled from each other by the present component-decoupling approach. Then all quantities, including pressure, conformation tensor and velocity, can be resolved without iteration. Additionally, the accuracy corrector is proposed to access the prior scheme limiter-estimation problem introduced by the implicit high-resolution scheme. We numerically demonstrate that all quantities preserve the second-order accuracy in time and space as expected by the theoretical splitting errors. Finally, several different types of canonical benchmark flow examples are conducted to validate the present solver, including laminar flow, turbulent drag-reducing flow and the rotation of a spherical particle immersed in a sheared viscoelastic fluid. • Two different pressure-conformation tensor-velocity and conformation tensor-components decoupling procedures are proposed. • All nonlinear terms in the governing equations are solved without iteration. • All flow quantities can be resolved without iteration in the present decoupling approach. • Both linear and nonlinear constitutive equations can be decoupled implicitly by the present procedure. • Implementation of high-resolution scheme for non-iterative implicit method is presented. [ABSTRACT FROM AUTHOR]

Large-scale modeling and predictive simulations of the subsurface flow and reactive transport system in porous media is significantly challenging, due to the high nonlinearity of the governing equations and the strong heterogeneity of material coefficients. The design of novel mathematical models and state-of-the-art methods for the flow simulation through porous media typically needs to satisfy the so-called bound-preserving property, i.e., the computed solution should stay inside a physically meaningful range. This paper presents a robust, scalable numerical framework based on the variational inequality formulation and the semismooth Newton method in a fully implicit manner, to model and simulate highly nonlinear flows without violating the boundedness requirement of the solution. Rigorous theoretical analysis for the variational inequality formulation of the problem is provided for facilitating the design of algorithms. Specifically, our approach further enhances the numerical formulation by utilizing a family of multilevel monolithic overlapping Schwarz methods for efficiently preconditioning, and the parallel implementation of the bound-preserving solver is based on the fast and robust domain decomposition technique. Numerical experiments are presented to demonstrate the efficiency and parallel scalability of the solution strategy for both standard benchmarks as well as realistic flow problems involving strong heterogeneity and high nonlinearity. We also show that the proposed framework is more robust and efficient than the commonly used inexact Newton algorithm in terms of the bound-preserving property. • Variational inequality discretization is proposed for reservoir flows. • Semismooth Newton algorithm is provided for the bound-preserving solution. • Multilevel domain decomposition is presented for preconditioning. • The proposed framework is highly scalable on the Tianhe-2 supercomputer. [ABSTRACT FROM AUTHOR]

The simulation of turbulent flow that involves scalar transport at high Schmidt or Prandtl numbers is a major challenge. Enhanced Schmidt and Prandtl numbers demand an excessive increase in numerical resolution. Otherwise, the accuracy of transport would suffer substantially through unresolved information and numerical diffusion. With the aim of providing an efficient alternative for such applications, this paper presents a simulation method that is based on a novel Eulerian-Lagrangian decomposition principle (ELD) of the transported quantity. Low-pass filtering of the initial scalar quantity field separates it into a smooth low-frequency component and a fine-structured high-frequency component. The low-frequency component is represented and transported according to the Eulerian description by applying the Finite Volume Method (FVM) with a numerical resolution according to the Kolmogorov scale. The high-frequency component is translated into the Lagrangian description by the formation of particles, which are transported in parallel. By exchanging information between the two components, a re-initialisation mechanism ensures that the frequency-based decomposition is maintained throughout the simulation. Such ELD approach combines the efficiency of the FVM with the numerical stability of Lagrangian particles. As a result of the frequency-separation, the latter are by principle limited to zones of small scales and thus effectively complement the FVM. Furthermore, the particle information allows details of the scalar quantity field to be reconstructed that extend into the sub-grid level. By using a mixing layer setup, the proposed method is tested for a range of Schmidt numbers, and the numerical costs are considered and discussed. • The transport of scalar quantities at high Schmidt numbers is becoming an increasingly important phenomenon in science. • Their accurate numerical simulation is extremely costly with the methods and resources that are currently available. • The combination of FVM with particle methods is a promising approach provided that the integration is well designed. • A concentrated use of particles in regions where they provide a substantial gain in resolution ensures numerical efficiency. [ABSTRACT FROM AUTHOR]

• Numerical dissipation modification to SLAU2 flux is proposed to avoid negative pressure at gas-liquid interfaces. • The modification does not involve any iterative or tunable parameters in AUSM+-up(f). • The modified SLAU2 flux allows stable and high-resolution results in multiphase flows. This paper proposes a novel method for the computation of compressible multiphase flows under the assumption of pressure equilibrium based on a 6-equation model and the AUSM (Advection Upstream Splitting Method) family. In this study, we introduce a new numerical pressure flux dissipation term based on the relative velocities in the gas and liquid phases to develop an analogous carbuncle-suppression mechanism that is applicable to gas dynamics. We also propose a mass flux dissipation term based on the pressure ratio at the gas-liquid interface and incorporate both terms into SLAU2, an AUSM-family scheme, to achieve robustness against shock anomalies. [ABSTRACT FROM AUTHOR]

Classical Multiscale Finite Volume (MsFV) methods can produce highly oscillatory pressure solutions (i.e., non-monotonic) for media with high permeability contrasts. This may lead to the production of spurious pressure fields, leading, for instance, to the appearance of gas throughout the reservoir when the pressure erroneously falls below the bubble point pressure, substantially increasing the computational cost to solve the problem due to the necessity of using iterative correction procedures to improve the solution. In this context, in the present paper, we propose an adaptive flow-based dual volume agglomeration strategy for correcting the non-physical terms in the coarse transmissibility matrix by means of a preprocessing local step. These terms can be seen as negative transmissibilities on the coarse scale mesh generated by huge permeability contrasts on the boundaries of the dual mesh. This is done by using a local recalculation of the basis functions in a patch defined by a judicious merging of dual coarse volumes that substantially reduces the spurious oscillations. Classical multilevel and multiscale methods define a uniform level at each coarse control volume, i.e., the same mesh level is used at each coarse control volume. As a result, in multiphase flow problems, there is a necessity to include volumes that do not contain the saturation front in the high-resolution level. To handle this problem, we also present a framework to deal with non-uniform levels at each coarse control volume, which allows the use of fine-scale control volumes only where it is needed, in order to produce smaller coarse scale matrices than those obtained from classical multilevel and multiscale methods. The proposed methodologies were applied to approximate pressure solutions in an Implicit Pressure Explicit Saturation (IMPES) strategy. In the present work, the flow problem is implicitly solved on the multilevel resolution and the transport problem is explicitly solved on the fine-scale. Our strategy was tested with two well-known challenging benchmark problems in order to show its accuracy and efficiency. [ABSTRACT FROM AUTHOR]

In this paper we address the compressible Navier–Stokes equations written in the so-called conservative formulation. In particular, we focus on the possibility of uncoupling the computation of the problem unknowns, namely, density, linear momentum and total energy, a technique usually labeled as fractional step method, which allows to reduce the associated computational cost. The proposed methodology is a finite-element solver supplemented with a stabilization technique within the Variational Multi-Scale framework. In this regard, we consider orthogonal and dynamic definitions for the subscales. This discretization in space shows an adequate stability, permitting in particular the use of equal interpolation for all variables in play. However, we complement it with a shock-capturing operator in order to solve problems involving shocks. Several representative benchmark flow simulations are performed, which demonstrate the suitability of the proposed algorithm for a vast range of regimes. • Novel fractional step method for compressible flows in conservative variables. • Scheme (of first and second order) designed at the algebraic level. • A stabilized finite element method is employed. • A shock capturing technique is introduced to deal with the appearance of shocks. • Numerical experiments show the excellent performance of the formulations proposed. [ABSTRACT FROM AUTHOR]

• Existing methods are described in consistent notations, with focus on error control. • A preliminary validation case enables to rule out methods not usable in practice. • A comparison on randomly-generated arrays of spheroids enables to determine which method is the most efficient in average. A review of the existing methods to compute the minimal distance between two ellipsoids has been conducted in order to retain the most adequate one within the context of Particle-Resolved Direct Numerical Simulations for particle-laden flows. First, all methods have been implemented and the corresponding algorithms are reported. Furthermore, a procedure has been systematically suggested to control the error associated with each method, when such control was not explicitly available. In a second phase, a two-ellipsoid configuration where an analytical solution is known has been used to perform an error study. This allows to assess the accuracy and consistency of each method, regarding required criteria defined in this paper. The methods that do not verify these criteria have been ruled out. Finally, the remaining methods have been studied on a benchmark of randomly-generated arrays of mono-dispersed spheroids, with aspect ratios ranging from 1 6 to 6 and volume fractions ranging from 0.05 to 0.25. For each method, the spheroidal packings have been sized to measure a statistically significant computing time. Such procedure enabled to study with generality the computing-time dependency of one method on the aspect ratio, the volume fraction, and the desired accuracy. The most efficient method for a given value of these parameters has then been identified. [ABSTRACT FROM AUTHOR]

• Compute two-phase flows with no spurious currents. • Instead of spurious currents, low-amplitude capillary waves at the inter- face are computed. • New fractional-step algorithm that is able to capture pressure jump due to surface tension accurately. • Handles extremely high density ratios above 1,000,000,000 and extremely high surface-tension constants above 500 N/m without spurious currents. Using current cell-centered numerical methods to calculate two-phase flows result in spurious currents developing at the interface between both phases when the capillary number is low enough. Treatments of the interface such as: computing surface tension more accurately, smoothing of the indicator function, and balancing the pressure and surface tension, are often used to reduce spurious currents. These treatments can affect the physics of the interface, and these approaches struggle when the density ratios are high or when the meshes are distorted. This paper presents a methodology that uses a moving unstructured staggered mesh that can handle extremely high-density ratios of at least 1,000,000,000 and extremely high surface tensions of at least 500 N/m without generating spurious currents. Instead of spurious currents, only physically correct low-amplitude and low energy capillary waves at the interface result from the errors in the surface discretization. The method is demonstrated on 2D static and dynamic droplet cases. [ABSTRACT FROM AUTHOR]

This paper describes a novel 2nd order direct forcing immersed boundary method designed for simulation of 2D and 3D incompressible flow problems with complex immersed boundaries. In this formulation, each cell cut by the immersed boundary (IB) is reshaped to conform to the shape of the IB. IBs are modeled as a series of 2D planes in 3D space that connect seamlessly at the edges of the cut cells, in a way that mimics conformal grid. IBs are represented in a continuous and consistent fashion from one cell to another, thus eliminating spatial pressure oscillations originating from inconsistent description of the IB as well as the traditional stair-step problem, leading to a more accurate resolution of the boundary layer. Boundary conditions are enforced at the exact location of the IB devoid of interpolation, which guarantees sound simulations even on grids with high aspect ratio, and enables simulations of flow packed with multiple IBs in close proximity. Boundary conditions for each phase across the IB are enforced independently, yielding a unique capability to solve flows with zero-thickness IBs. Simulations of a large number of 2D and 3D test cases confirm the prowess of the devised immersed boundary method in solving flows over multiple loosely/closely-packed IBs; stationary, moving and highly morphing IBs; as well as IBs with zero-thickness. Results show that predictions from the proposed scheme agree remarkably well with theoretical models and experimental data for both integral variables and local flow fields and they are often with less than 1% deviation from solutions obtained by conformal grid of similar resolution. [ABSTRACT FROM AUTHOR]

• Construction of high-order instantaneous pressure estimates from the average pressure. • In-situ or offline calculations of pressure estimates. • General formulas for the construction of pressure estimates. • The estimates are independent of boundary conditions, discretization, and mesh type. We derive high-order estimates of the instantaneous pressure for projection-type solvers of the incompressible Navier-Stokes equations. Projection methods play a central role in incompressible and low-Mach fluid flow simulations. However, these methods are known to produce a first-order instantaneous pressure at the end of a timestep, even when used with high-order integrators such as Runge-Kutta or Adams-Bashforth methods. In many instances, a high-order pressure is needed when the application demands it, such as turbulent aerodynamic flows, fluid-structure interaction, membrane filtration, and pressure-dependent boundary conditions. The common strategy to circumvent this limitation is to perform a so-called "post-processing" projection which results in an instantaneous pressure of the same order as the time integrator. However, this additional projection adds more cost to a simulation, especially in the context of high-performance computing. For example, in a third-order Runge-Kutta integration, requiring a post-processing projection increases the computational cost by 33%. Therefore, it is desirable to find high-order consistent estimates for the instantaneous pressure without the need for a post-processing projection. In this paper, we introduce a novel approximation to compute high-order estimates for the instantaneous pressure for arbitrary high-order time integrators, without the need for a post-processing projection. Our proposed approximations are independent of the time integration methodology or boundary conditions. We validate our results using various implicit and explicit integrators on different benchmark problems with periodic and time-dependent boundary conditions. [ABSTRACT FROM AUTHOR]

The performance of high-order gas-kinetic scheme (HGKS) has been investigated for the direct numerical simulation (DNS) of isotropic compressible turbulence up to the supersonic regime [9]. Due to the multi-scale nature and coupled temporal-spatial evolution process, HGKS provides a valid tool for the numerical simulation of compressible turbulent flow. Based on the domain decomposition and message passing interface (MPI), a parallel HGKS code is developed for large-scale computation in this paper. The standard tests from the nearly incompressible flow to the supersonic one, including Taylor-Green vortex problem, turbulent channel flow and isotropic compressible turbulence, are presented to validate the parallel scalability, efficiency, accuracy and robustness of parallel implementation. The performance of HGKS for the nearly incompressible turbulence is comparable with the high-order finite difference scheme, including the resolution of flow structure and efficiency of computation. Based on the accuracy of the numerical solution, the numerical dissipation of the scheme in the turbulence simulation is quantitatively evaluated. Meanwhile, based on the kinetic formulation HGKS shows advantage for supersonic turbulent flow simulation with its accuracy and robustness. The current work demonstrates the capability of HGKS as a powerful DNS tool from the low speed to supersonic turbulence study, which is less reported under the framework of finite volume scheme. • A parallel HGKS code is developed as a powerful DNS tool from the low speed to supersonic turbulence study. • The parallel scalability, efficiency, accuracy and robustness of parallel implementation of HGKS are validated. • The performance of HGKS for the nearly incompressible turbulence is comparable with the high-order finite difference scheme. • As a mesoscopic method, HGKS also performs better than both lattice Boltzmann method (LBM) and discrete unified gas-kinetic scheme (DUGKS). [ABSTRACT FROM AUTHOR]

• A multiple instance-solver framework is presented for multi-component moving configurations. • The framework can automatically instantiate multiple full-functional solvers from one template solver. • The array configuration flow can be solved by multiple instance-solvers in a one-to-one correspondence manner. • The framework is parallel, modular, automated, and easily extended to multi-disciplinary solvers. This paper presents a novel computational fluid dynamics (CFD) framework for flow simulation of complex configurations containing relatively moving components. The framework is based on the dynamic overset grid method and is intrinsically parallel. The user only needs to decompose complex configurations into topologically simple components according to the geometric features and generate high-quality computational meshes around these components. The framework can then automatically instantiate multiple fully functional CFD solvers to solve the flow fields on the meshes of all components simultaneously in a one-to-one correspondence. Thus, the geometric relationships of the components are transformed into concurrent states of the instance solvers, and accordingly, their flow fields are coupled through the intercommunication among instance solvers. The framework is implemented in a parallel environment based on the Message Passing Interface (MPI). An instantiation space is formed by splitting the world communicator into desired number of fully functional sub-communicators. Within this space, the same number of independent solvers with complete input and output interfaces can be instantiated from the same template solver. The data coupling between instance solvers is realised using the dynamic overset grid method, and the whole process is achieved automation by approaches of collision detection, Exact Inverse Maps (EIM)-based donor cell search, and robust Implicit Hole Cutting (IHC). Numerical results show that the framework is effective for configurations with complex topologies, and it is particularly suitable for numerical simulations of array configurations with relatively moving components. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the theoretical interpretation of the artificial compressibility method (ACM) to propose a new explicit method for the unsteady numerical simulation of fluid flow. The proposed method employs the compressible continuity and Navier–Stokes equations, which facilitates the replacement of pressure as one of the major variables with density, theoretically backed by virtual particle concept. This new concept justifies the theoretical treatment assuming the speed of sound in ACM as a model parameter determined by the grid system. More importantly, the present method realizes, in a fully explicit manner, the solving of a set of equations, which prevents the solving of the Poisson equation of pressure. The new method was validated and proven by comparing the results of two-dimensional cavity flow between the proposed method, conventional incompressible method, and the Lattice–Boltzmann method with varying Reynolds numbers (100, 1000, and 10000). The results of the proposed method agree well with conventional and reference data for both steady-state and unsteady-state conditions, although slight numerical oscillations were observed for the proposed method at a Reynolds number of 10000. Thus, the numerical validation assures that the proposed method is an explicit method based on a solid theoretical ground to be a new efficient simulation framework. • The theoretical interpretation of an artificial compressibility method is discussed. • An explicit numerical simulation for fluid flow was proposed. • Theoretical reasons were explained to assume speed of sound as a numerical parameter. • Two-dimensional cavity flow was simulated to verify the proposed method. [ABSTRACT FROM AUTHOR]

• Development of unified gas-kinetic wave-particle method for diatomic gas. • The multiscale solution is captured through dynamic adaptation of wave and particle formulation. • UGKWP becomes particle method in rarefied regime and hydrodynamic solver in continuum regime. • UGKWP keeps optimal efficiency in different flow regimes for the hypersonic flow simulation. In this paper, the unified gas-kinetic wave-particle (UGKWP) method is further developed for diatomic gas with the energy exchange between translational and rotational modes for flow study in all regimes. The multiscale transport mechanism in UGKWP is coming from the direct modelling in a discretized space, where the cell's Knudsen number, defined by the ratio of particle mean free path over the numerical cell size, determines the flow physics simulated by the wave particle method. The non-equilibrium distribution function in UGKWP is tracked by the discrete particle and analytical wave. The weights of distributed particle and wave in different regimes depend on cell's Knudsen number, where distinguishable macroscopic flow variables of particle and wave are updated inside each control volume. The UGKWP becomes a particle method in the highly rarefied flow regime and converges to the gas-kinetic scheme (GKS) for the Navier-Stokes solution in the continuum flow regime without particles. In comparison with discrete velocity method (DVM)-based unified gas-kinetic scheme (UGKS), the computational cost and memory requirement in UGKWP have been reduced by several orders of magnitude for the high speed and high temperature flow simulation, where the translational and rotational non-equilibrium can be captured accurately in the transition and rarefied regime. As a result, for the hypersonic flow around a flying vehicle, the computation can be conducted using a personal computer for the studies in all regimes. The UGKWP method for diatomic gas will be validated in various cases from one dimensional shock structure to three dimensional flow over a sphere, and the numerical solutions will be compared with the reference DSMC results and experimental measurements. [ABSTRACT FROM AUTHOR]

• A novel volume-preserving reference map method. • Uses the local deviation from the volume-preserving space to reduce the mass loss. • The correction is the projection on the space of volume-preserving diffeomorphisms. • Substantial mass loss reduction for practical applications such as two-phase flows. This paper presents an implicit interface representation, where the geometry is captured by a level set function and its deformations are reconstructed from diffeomorphism between the warped and original geometries (the reference map). A key advantage of this representation is that it provides a local estimation of numerical local mass losses. Using this metric, we design a novel projection for the reference map on the space of volume-preserving diffeomorphisms which results in enhanced, but inexact, mass conservation. In the limit of small deviations from this space, the projection is shown to be uniquely defined, and the correction can be computed as the solution of a Poisson problem. The method is analyzed and validated in two and three spatial dimensions. Both the theoretical and computational results show it excels at correcting the mass loss due to inaccuracy in the advection process or the velocity field. While this error reduction does not manifest for analytical problems, it is evident for practical applications such as the simulation of multiphase flows over long time intervals and offers improved computational exploration capabilities. [ABSTRACT FROM AUTHOR]

This paper extends the second-order accurate BGK finite volume schemes for the ultra-relativistic flow simulations [5] to the 1D and 2D special relativistic hydrodynamics with the Synge equation of state. It is shown that such 2D schemes are very time-consuming due to the moment integrals (triple integrals) so that they are no longer practical. In view of this, the simplified BGK (sBGK) schemes are presented by removing some terms in the approximate nonequilibrium distribution at the cell interface for the BGK scheme without loss of accuracy. They are practical because the moment integrals of the approximate distribution can be reduced to the single integrals by some coordinate transformations. The relations between the left and right states of the shock wave, rarefaction wave, and contact discontinuity are also discussed, so that the exact solution of the 1D Riemann problem could be derived and used for the numerical comparisons. Several numerical experiments are conducted to demonstrate that the proposed gas-kinetic schemes are accurate and stable. A comparison of the sBGK schemes with the BGK scheme in one dimension shows that the former performs almost the same as the latter in terms of the accuracy and resolution, but is much more efficient. [ABSTRACT FROM AUTHOR]

In this paper a fully Eulerian solver for the study of multiphase flows for simulating the propagation of surface gravity waves over submerged bodies is presented. We solve the incompressible Navier–Stokes equations coupled with the volume of fluid technique for the modeling of the liquid phases with the interface, an immersed body method for the solid objects and an iterative strong–coupling procedure for the fluid–structure interaction. The flow incompressibility is enforced via the solution of a Poisson equation which, owing to the density jump across the interfaces of the liquid phases, has to resort to the splitting procedure of Dodd and Ferrante [1]. The solver is validated through comparisons against classical test cases for fluid–structure interaction like migration of particles in a pressure–driven channel, multiphase flows, 'water exit' of a cylinder and a good agreement is found for all tests. Furthermore, we show the application of the solver to the case of a surface gravity wave propagating over a submerged reversed pendulum and verify that the solver can reproduce the energy exchange between the wave and the pendulum. Finally the three–dimensional spilling breaking of a wave induced by a submerged sphere is considered. [ABSTRACT FROM AUTHOR]

• An efficient algorithm for inspecting pairs of particles for collisions is developed. • The method exploits the geometric mapping from reference to physical space. • Computational cost can be significantly reduced compare to standard approaches. • An enhanced particle-wall collision algorithm for curved elements is proposed. • Hypersonic dusty flow and surface erosion by sandblasting are simulated. This paper discusses the development of algorithms for simulating compressible, four-way coupled, particle-laden flows with discontinuous Galerkin methods. Specifically, the algorithmic developments focus on the treatment of hard-sphere collisions. First, we aim to reduce the computational effort devoted to inspecting pairs of particles for collisions during the given time step. This is often one of the most expensive stages of four-way coupled particle-laden flow simulations. The proposed algorithm exploits information about relative particle positions provided by the geometric mapping of a physical element to a reference element commonly employed in discontinuous Galerkin and other finite-element-based solvers. Second, we develop an enhanced particle-wall collision methodology that better accounts for finite particle size than previously developed schemes. A particular feature of the particle-particle and particle-wall collision algorithms is compatibility with arbitrary, curved, unstructured elements. Finally, we apply the resulting framework to a number of test cases, including hypersonic dusty flow over an entry capsule and surface erosion by sandblasting. [ABSTRACT FROM AUTHOR]