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With the WENO reconstruction, a third-order multidimensional gas-kinetic scheme, with inclusion of both normal and tangential derivatives of macroscopic flow variables, is constructed for the three-dimensional inviscid and viscous flow computations. For the flux evaluation, a time and space dependent gas distribution function from an initial piece-wise discontinuous polynomials around a cell interface is presented, where a multiple scale physical process from the kinetic to the hydrodynamic one is used for the flow evolution process. A high-order accuracy is achieved in the current scheme by integrating the space and time dependent flux function over the surface of a cell interface and a whole time step, without using the conventional Gaussian points integration for spatial accuracy and Runge–Kutta method for temporal accuracy, which have been used in many other high-order schemes. This scheme is applied to both inviscid and viscous, and low and high speed flow computations. The numerical tests clearly demonstrate that the current scheme is robust for the flows with strong discontinuities and accurate for viscous smooth flow solutions. The continuous effort on the gas kinetic scheme (GKS) is to develop a third method which has the same reliability and robustness as the well-developed second-order shock capturing schemes, but is simply much more accurate in all flow applications. The current scheme seems achieve such a target. [ABSTRACT FROM AUTHOR]

A new algorithm for the computing of compressible flows governed by Euler/Navier–Stokes equations is presented in this paper. The inter-cell numerical convective flux is estimated through a weighted combination of fourth order central/third order upwind biased/first order upwind interpolations of inter-cell numerical fluid velocity and convective transport vector. The higher order/lower order interpolations are carefully combined via two types of local solution sensitive weight functions. One of the weight functions is designed to control the balance of upwind/central contributions via flow speeds while the other one performs the dual purpose of detecting non-smooth or discontinuous features in the solution and regulating the balance between the higher order and first order upwind interpolations. The present work, through several one-dimensional (scalar and vector hyperbolic conservation laws) and multi-dimensional (Euler/Navier–Stokes) test cases, demonstrates that a carefully designed flux-based scheme can deliver a comparable performance in terms of robustness, accuracy and efficiency and is much simple to implement in comparison to some of the popular wave based TVD schemes like Van Leer and AUSMPW+ of Flux-Vector Splitting type and HLL scheme of Reconstruction-Evolution (Godunov) type. Employing multi-dimensional test cases, it is shown that, the new scheme is very robust and can be utilized for computing flows over a very wide range of flow speeds, ranging from incompressible limit (Mach No. ∼0.1) to very high speed compressible flows (Mach No. ∼10). [ABSTRACT FROM AUTHOR]

Iterative methods based on block incomplete LU (BILU) factorization are considered highly effective for solving large-scale block-sparse linear systems resulting from coupled PDE systems with n equations. However, efforts on porting implicit PDE solvers to massively parallel shared-memory heterogeneous architectures, such as general-purpose graphics processing units (GPGPUs), have largely avoided BILU, leaving their enormous performance potential unfulfilled in many applications where the use of implicit schemes and BILU-type preconditioners/solvers is highly preferred. Indeed, strong inherent data dependency and high memory bandwidth demanded by block matrix operations render naive adoptions of existing sequential BILU algorithms extremely inefficient on GPGPUs. In this study, we present a fine-grained BILU (FGBILU) scheme which is particularly effective on GPGPUs. A straightforward one-sweep wavefront ordering is employed to resolve data dependency. Granularity is substantially refined as block matrix operations are carried out in a true element-wise approach. Particularly, the inversion of diagonal blocks, a well-known bottleneck, is accomplished by a parallel in-place Gauss–Jordan elimination. As a result, FGBILU is able to offer low-overhead concurrent computation at O ( n 2 N 2 ) scale on a 3D PDE domain with a linear scale of N . FGBILU has been implemented with both OpenACC and CUDA and tested as a block-sparse linear solver on a structured 3D grid. While FGBILU remains mathematically identical to sequential global BILU, numerical experiments confirm its exceptional performance on an Nvidia GPGPU. [ABSTRACT FROM AUTHOR]

Abstract: This paper describes the implicit MacCormack scheme in finite volume formulation. Unsteady flows with moving boundaries are considered using arbitrary Lagrangian–Eulerian approach. The scheme is unconditionally stable and does not require solution of large systems of linear equations. Moreover, the upgrade from explicit MacCormack scheme to implicit one is very simple and straightforward. Several computational results for 2D and 3D flows over profiles and wings are presented for the case of inviscid and viscous flows. [Copyright &y& Elsevier]

Abstract: A new cell centred Lagrangian Godunov scheme for shock hydrodynamics is proposed. The new method uses a transient dual grid to define the motion of the vertices in a way that is consistent with the geometric conservation law. [Copyright &y& Elsevier]

The Chimera overset method is a powerful technique for modeling fluid flow associated with complex engineering problems. The use of structured meshes has enabled engineers to develop a number of high-order schemes, such as the WENO and compact differencing schemes. This paper demonstrates a Discontinuous Galerkin (DG) scheme with a Chimera overset method applied to viscous meshes on curved geometries. The small stencil of the DG scheme makes it particularly suitable for Chimera meshes. The small stencil simplifies the hole cutting and partitioning of grids that contain holes. In addition, because the DG scheme represents the solution as cell local polynomials, it does not require an interpolation scheme with a large stencil to establish the inter-grid communication in overlapping regions. Furthermore, the DG scheme is capable of using curved cells to represent geometric features. The curved cells resolve issues associated with linear non-co-located Chimera viscous meshes used for finite volume and finite difference schemes. The DG-Chimera method is demonstrated on a set of viscous Chimera meshes, which would produce erroneous results for a finite volume or finite difference scheme without corrections to the interpolation. [ABSTRACT FROM AUTHOR]

Explicit Runge–Kutta method has been widely used for time-accurate simulations in aeroacoustics and aerodynamics, partly because of its strong stability properties. However, when dealing with problems involving irregular geometries or multi-scale phenomena where the grid is often refined in localized regions, a single global time step size dictated by the smallest grid size based on the explicit stability condition would inevitably result in excessive computational consumption. A local time stepping strategy that adopts time step size to the local stability requirement in different grid blocks is an effective way to reduce the cost of time integration and to increase the overall computational efficiency. In the present paper, a non-uniform time step (NUTS) explicit Runge–Kutta scheme, previously introduced in the framework of discontinuous Galerkin method, which makes the local time stepping strategy applicable to the explicit Runge–Kutta family without any interpolation and extrapolation in time, is further extended to high-order finite difference methods. The stability of non-uniform time step (NUTS) scheme in combination with high order difference schemes is studied. Numerical experiments are carried out using 1D and 2D acoustic problems for validation of the proposed approach. Computational cost reduction by the proposed algorithm is also discussed. [ABSTRACT FROM AUTHOR]

The influence of numerical dissipation on direct numerical simulation (DNS) of decaying isotropic turbulence and turbulent channel flow is investigated respectively by using the seventh-order low-dissipation monotonicity-preserving (MP7-LD) scheme with different levels of bandwidth dissipation. It is found that for both benchmark test cases, small-scale turbulence fluctuations can be largely suppressed by high level of scheme dissipation, while the appearance of numerical errors in terms of high-frequency oscillations could destabilize the computation if the dissipation is reduced to a very low level. Numerical studies show that reducing the bandwidth dissipation to 70% of the conventional seventh-order upwind scheme can maximize the efficiency of the MP7-LD scheme in resolving small-scale turbulence fluctuations and, in the meantime preventing the accumulation of non-physical numerical errors. By using the optimized MP7-LD scheme, DNS of an impinging oblique shock-wave interacting with a spatially-developing turbulent boundary layer is conducted at an incoming free-stream Mach number of 2.25 and the shock angle of 33.2°. Simulation results of mean velocity profiles, wall surface pressure, skin friction and Reynolds stresses are validated against available experimental data and other DNS predictions in both the undisturbed equilibrium boundary layer region and the interaction zone, and good agreements are achieved. The turbulence kinetic energy transport equation is also analyzed and the balance of the equation is well preserved in the interaction region. This study demonstrates the capability of the optimized MP7-LD scheme for DNS of complex flow problems of wall-bounded turbulent flow interacting with shock-waves. [ABSTRACT FROM AUTHOR]

Highlights: [•] A Chimera method based on a Discontinuous Galerkin discretization is presented. [•] DG-Chimera does not need fringe points used in finite volume Chimera methods. [•] Grid generation is significantly simpler due to the lack of fringe points. [•] Hole cutting procedures can be performed without regard to stencils. [•] DG-Chimera is demonstrated to be consistent and verified using inviscid flow problems. [Copyright &y& Elsevier]

Abstract: This study presents a new weighted compact nonlinear scheme (WCNS). In the WCNS procedure, the linear difference scheme is modified to use the flux on the computational nodes together with that on the midpoints. This modification makes the scheme more robust, but at the same time, more dissipative. We conduct the truncation error analysis and discuss the reasons why this modification makes the scheme robust and dissipative. The standard shock problems are solved with both original and modified WCNS, and the results show that the discontinuity thickness of the modified WCNS increases, and over/undershoots at the discontinuities are suppressed better in WCNS. In addition, the stiff shock tube problems, which cannot be solved by the original WCNS because of negative pressure, can be solved using the modified WCNS without a blow-up of computation. A series of numerical tests show the robustness of the modified WCNS. [Copyright &y& Elsevier]

In this paper, a new numerical approach for the steady incompressible turbulent flows is investigated. The artificial compressibility method (ACM) is applied to the Reynolds Averaged Navier-Stokes (RANS) equations. A new Characteristic-Based Turbulent (CBT) scheme is developed for the convective fluxes. The well-known Spalart–Allmaras turbulence model is employed to check the effectiveness of this new scheme. Comparing the proposed scheme with previous studies, it is found that the present CBT scheme demonstrates accurate results, high stability and faster convergence. In addition, the local time stepping and implicit residual smoothing are applied as the convergence acceleration techniques. The turbulent flows past a backward facing step, circular cylinder, and NACA0012 hydrofoil are studied as benchmarks. Results compare favorably with those of other available schemes. [ABSTRACT FROM AUTHOR]

Numerical investigations of the launch process of a base bleed projectile from the muzzle to free-flight stage have been performed in this paper. A dynamic overlapped grids approach was applied to deal with the problems of a high-speed moving base bleed projectile. A high-resolution upwind scheme (AUSMPW+) and detailed reaction kinetics model were employed to solve the chemical non-equilibrium Euler equations for dynamic grids. A typical case was calculated for the verification of the dynamic overlapped grids approach and numerical methods solving the chemical non-equilibrium flows. After good agreement was achieved, the development process of muzzle flows with high-speed moving base bleed projectile and the rapid depressurization process in the combustion chamber of base bleed unit are discussed in detail. This present numerical study confirms that complicated transient phenomena exist in the early launch stages after the base bleed projectile moves from the muzzle of cannon to the free-flight stage. The base bleed unit of projectile undergoes a strong non-steady-state rapid depressurization. This paper is a significant investigation for understanding muzzle flows with base bleed projectile and rapid depressurization in the combustion chamber of base bleed unit, which can provide valuable reference data for research on combustion stability of the propellant in the combustion chamber. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the collocated method of MCIM (Mass Corrected Interpolation Method) is employed for solving two-dimensional incompressible flows on unstructured grid systems. A control-volume-based finite element (CVFEM) approach has been taken in which conservation equations are formed for each control volume throughout the solution domain. In this study, three different algorithms are proposed and investigated. In the first algorithm a fully coupled formulation is used, however in the second algorithm a segregated approach without pressure correction is employed. In the third solution algorithm, the scheme of MCIM is implemented to SIMPLE-like segregated algorithm. The linear system of equations obtained in these algorithms is solved using a direct sparse solver. The accuracy and performance of the proposed algorithms are demonstrated by solving different steady and unsteady benchmark problems. [Copyright &y& Elsevier]

Abstract: A computational investigation of the effects on parallel performance of higher-order accurate schemes was carried out on two different computational systems: a traditional CPU based MPI cluster and a system of four Graphics Processing Units (GPUs) controlled by a single quad-core CPU. The investigation was based on the solution of the level set equations for interface tracking using a High-Order Upstream Central (HOUC) scheme. Different variants of the HOUC scheme were employed together with a 3rd-order TVD Runge–Kutta time integration. An increase in performance of two orders of magnitude was seen when comparing a single CPU core to a single GPU with a greater increase at higher orders of accuracy and at lower precision. [Copyright &y& Elsevier]

Abstract: We present a one-step high-order cell-centered numerical scheme for solving Lagrangian hydrodynamics equations on unstructured grids. The underlying finite volume discretization is constructed through the use of the sub-cell force concept invoking conservation and thermodynamic consistency. The high-order extension is performed using a one-step discretization, wherein the fluxes are computed by means of a Taylor expansion. The time derivatives of the fluxes are obtained through the use of a node-centered solver which can be viewed as a two-dimensional extension of the Generalized Riemann Problem methodology introduced by Ben-Artzi and Falcovitz. [Copyright &y& Elsevier]

Abstract: A novel multi-block compact-TVD finite difference method for the simulation of compressible flows is presented. The method combines distributed and shared-memory paradigms to take advantage of the configuration of modern supercomputers that host many cores per shared-memory node. In our approach a domain decomposition technique is applied to a compact scheme using explicit flux formulas at block interfaces. This method offers great improvement in performance over earlier parallel compact methods that rely on the parallel solution of a linear system. A test case is presented to assess the accuracy and parallel performance of the new method. [Copyright &y& Elsevier]

Abstract: Following Sun’s approach , Shuman smoothing instead of conventional diffusion terms is used in a simple two-time step semi-implicit finite volume scheme to simulate dam break. When the Courant number is less than one, the absolute value of amplification factor of the 1D linearized shallow-water equations is 1 in this new scheme. Compared with the characteristic-based semi-Lagrangian schemes and the Riemann solver, this scheme produces excellent results of free water depth and speed of the shock. Numerical simulations show that the water inside the dam initially moves away radially until water almost depletes near the center; then the water moves back to the center and forms a vertical water column there. This paper proves that Shuman smoothing can be used not only in the linearized shallow-water equations discussed in Sun but also in the nonlinear wave equations to control instability around shocks. [Copyright &y& Elsevier]