Implementation of the low Mach number method for calculating flows in the NOISEtte software package

This paper is devoted to the development of computational techniques for simulating low Mach number flows on unstructured meshes based on the Roe method and the edge-based vertexcentered higher accuracy schemes. The techniques are implemented in the in-house NOISEtte code. The results of predicting an inviscid compressible low Mach number flow over a NACA0012 airfoil are presented and analyzed. The computations are carried out on structured and unstructured triangular grids.     

A hybrid numerical method and its application to inviscid compressible flow problems

An improved version of the artificially upstream flux vector scheme, is developed to efficiently compute inviscid compressible flow problems. This numerical scheme, named AUFSR (Tchuen et al. 2011), is obtained by hybridizing the AUFS scheme with Roe’s solver. This approach handles difficulties encountered by the AUFS scheme, in the case where the flux vector does not check the homogeneous property. The present scheme for multi-dimensional flows introduces a certain amount of numerical dissipation to shear waves, as Roe’s splitting. The AUFSR scheme is not only robust for shock-capturing, but also accurate for resolving shear layers. Numerical results for 1D Riemann problems and several 2D problems are investigated to show the capability of the method to accurately compute inviscid compressible flow when compared to AUFS, and Roe solvers.     

A simple construction of very high order non-oscillatory compact schemes on unstructured meshes

In [Abgrall R, Roe PL. High order fluctuation schemes on triangular meshes. J Sci Comput 2003;19(1-3):3-36] have been constructed very high order residual distribution schemes for scalar problems. They were using triangle unstructured meshes. However, the construction was quite involved and was not very flexible. Here, following [Abgrall R. Essentially non-oscillatory residual distribution schemes for hyperbolic problems. J Comput Phys 2006;214(2):773-808], we develop a systematic way of constructing very high order non-oscillatory schemes for such meshes. Applications to scalar and systems problems are given.     

A high efficiency parallel unstructured solver dedicated to internal combustion engine simulation

IFP-C3D, a hexahedral unstructured parallel solver dedicated to multiphysics calculation is being developed at IFP to compute the compressible combustion in internal engines. IFP-C3D uses an unstructured formalism, the finite volume method on staggered grid, time splitting, SIMPLE loop, subcycled advection, turbulent and Lagrangian spray and a liquid film model. Original algorithms and models such as the conditional temporal interpolation methodology for moving grids, the remapping algorithm for transferring quantities on different meshes during the computation enable IFP-C3D to deal with complex moving geometries with large volume deformation induced by all moving geometrical parts (intake/exhaust valve, piston). Large super-scalar machines up to 1000 processors are being widely used and IFP-C3D has been optimized for running on these Cluster machines. IFP-C3D is parallelized using the Message Passing Interface (MPI) library to distribute a calculation over a large number of processors. Moreover, IFP-C3D uses an optimized linear algebraic library to solve linear matrix systems and the METIS partitionner library to distribute the computational load equally for all meshes used during the calculation and in particular during the remap stage when new meshes are loaded. Numerical results and performance timing are presented to demonstrate the computational efficiency of the code.     

基于异构平台的通量分裂格式性能研究

通量分裂是在方程组条件下实现迎风特性的主要手段,为了实现典型通量分裂格式在CPU/GPU异构平台的性能分析。在NVIDIA GTX1660super上,使用统一设备计算架构(CUDA)编程模型实现一维欧拉求解器;以激波管Riemann问题为算例,对矢通量分裂格式van leer、通量差分分裂格式Roe以及混合通量分裂AUSMPW+进行计算分析;数值结果表明,三种格式在异构计算体系能够得到合理且可用的计算结果;Roe格式激波分辨率最高且在CPU/GPU体系加速效果最好;Van Leer激波分辨率较低于Roe和AUSMPW+,计算效率高但其格式构造中存在大量判断分支,影响了加速性能;AUSMPW+格式激波分辨率与Roe相当,加速性能略好于Van Leer。     

Second-order-accurate explicit fluctuation splitting schemes for unsteady problems

This paper is concerned with the issue of obtaining explicit fluctuation splitting schemes which achieve second-order accuracy in both space and time on an arbitrary unstructured triangular mesh. A theoretical analysis demonstrates that, for a linear reconstruction of the solution, mass lumping does not diminish the accuracy of the scheme provided that a Galerkin space discretization is employed. Thus, two explicit fluctuation splitting schemes are devised which are second-order accurate in both space and time, namely, the well known Lax-Wendroff scheme and a Lax-Wendroff-type scheme using a three-point-backward discretization of the time derivative. A thorough mesh-refinement study verifies the theoretical order of accuracy of the two schemes on meshes with increasing levels of nonuniformity.     

High-speed compressible flow solutions by adaptive cell-centered upwinding algorithm with modified H-correction entropy fix

Adaptive Delaunay triangulation is combined with the cell-centered upwinding algorithm to analyze high-speed compressible flow problems. The H-correction entropy fix is modified and included in the upwinding algorithm for unstructured triangular meshes to improve the computed shock wave resolution. The solution accuracy is further improved by coupling an error estimation procedure to a remeshing algorithm. Efficiency of the combined procedure is evaluated by analyzing supersonic shocks and shock propagation behaviors for both the steady and unsteady high-speed compressible flows.     

Third Order Accurate Non-Polynomial Reconstruction on Rectangular and Triangular Meshes

This paper presents a finite volume scheme on rectangular and triangular meshes based on a third order accurate logarithmic reconstruction. Several numerical experiments, including the Euler equations for compressible gas dynamics, illustrate the high resolution and non-oscillatory properties of the new scheme AMS: 35L65; 35L45; 65M06; 76N15     

On some approaches to solve CFD problems

This paper presents two efficient methods for spatial flows calculations. In order to simulate of incompressible viscous flows, a second-order accurate scheme with an incomplete LU decomposed implicit operator is developed. The scheme is based on the method of artificial compressibility and Roe flux-difference splitting technique for the convective terms. The numerical algorithm can be used to compute both steady-state and time-dependent flow problems. The second method is developed for modeling of stationary compressible inviscid flows. This numerical algorithm is based on a simple flux-difference splitting into physical processes method and combines a multi level grid technology with a convergence acceleration procedure for internal iterations. The capabilities of the methods are illustrated by computations of steady-state flow in a rotary pump, unsteady flow over a circular cylinder and stationary subsonic flow over an ellipsoid.     

A robust shock-capturing scheme based on rotated Riemann solvers

This paper presents a robust finite volume shock-capturing scheme based on the rotated approximate Riemann solver. A general framework for constructing the rotated Riemann solver is described and a rotated Roe scheme is discussed in detail. It is found that the robustness of the rotated shock-capturing scheme is closely related to the way in which the direction of upwind differencing is determined. When the upwind direction is determined by the velocity-difference vector, the rotated Roe scheme demonstrates a robust shock-capturing capability and the shock instabilities or carbuncle phenomena can be eliminated completely. The dissipation property associated with the linear field of the rotated flux-difference splitting scheme is analyzed, and several test cases are presented to validate the proposed scheme.     

Adaptive multiresolution for finite volume solutions of gas dynamics

Multiresolution analysis is used to improve the CPU and memory performance of a finite volume scheme. Departing from Harten's original scheme we present a fully adaptive scheme in the sense that at a given time, the solution is represented in a compressed form by a set of significant wavelet coefficients. Numerical benchmarks for Euler's system of compressible gas dynamics are performed on triangular meshes.     

Parallel adaptive simulations of dynamic fracture events

Finite element simulations of dynamic fracture problems usually require very fine discretizations in the vicinity of the propagating stress waves and advancing crack fronts, while coarser meshes can be used in the remainder of the domain. This need for a constantly evolving discretization poses several challenges, especially when the simulation is performed on a parallel computing platform. To address this issue, we present a parallel computational framework developed specifically for unstructured meshes. This framework allows dynamic adaptive refinement and coarsening of finite element meshes and also performs load balancing between processors. We demonstrate the capability of this framework, called ParFUM, using two-dimensional structural dynamic problems involving the propagation of elastodynamic waves and the spontaneous initiation and propagation of cracks through a domain discretized with triangular finite elements.     

Development of Roe-type scheme for all-speed flows based on preconditioning method

The problems of mixed low-speed/high-speed flows are not solved properly with existing compressible method. Based on preconditioning technology, a new scheme, All-Speed-Roe scheme, is proposed. Compared with Roe scheme, it decreases the effect of acoustic speed in its numerical dissipation when Mach numbers decrease. Compared with traditional preconditioned Roe scheme, it overcomes the limit of being cut-off by the global Mach number through modifying the eigenvalues only and has the good convergence acceleration rate for low-Mach-number flows through multiplying the spatial residual by the preconditioner. From another perspective, All-Speed-Roe scheme suggests that there is no necessity to replace the physical acoustic speed in denominator with pseudo-acoustic speed. In theory, All-Speed-Roe scheme is suitable for all speed flow calculations with capturing shock and simulating low-Mach-number flows. The numerical results of Euler nozzle flow, RANS of NASA rotor 37 flow, Euler simulation, Large Eddy Simulation (LES) and Detached Eddy Simulation (DES) of high-loaded blade T106 flow show that All-Speed-Roe scheme can replace traditional preconditioned Roe scheme because it is easier for programming, more robust in computations, more accurate in spatial, and has good convergence rate.     

Simulation of flowfields induced by wind blades based on a parallelized low-speed flow solver

In this study, a parallel computing technology is applied on the simulation of a wind turbine flow problem. A third-order Roe type flux limited splitting based on a pre-conditioning matrix with an explicit time marching method is used to solve the Navier–Stokes equations. The original FORTRAN code was parallelized with Message Passing Interface (MPI) language and tested on a 64-CPU IBM SP2 parallel computer. The test results show that a significant reduction of computing time in running the model and a super-linear speed up rate is achieved up to 32 CPUs at IBM SP2 processors. The speed up rate is as high as 49 for using IBM SP2 64 processors. The test shows very promising potential of parallel processing to provide prompt simulation of the current wind turbine problems.     

A Roe scheme for the Bi-temperature model of magnetohydrodynamics

In this paper, a Roe scheme for the bi-temperature magnetohydrodynamics (MHD) model is set up. A Roe matrix is obtained for the one-dimensional system in Eulerian coordinates. These results are extended to the two-dimensional case. One- and two-dimensional numerical examples are provided, showing Roe solver efficiency.     

Second-Order Accurate Godunov Scheme for Multicomponent Flows on Moving Triangular Meshes

This paper presents a second-order accurate adaptive Godunov method for two-dimensional (2D) compressible multicomponent flows, which is an extension of the previous adaptive moving mesh method of Tang et al. (SIAM J. Numer. Anal. 41:487–515, 2003) to unstructured triangular meshes in place of the structured quadrangular meshes. The current algorithm solves the governing equations of 2D multicomponent flows and the finite-volume approximations of the mesh equations by a fully conservative, second-order accurate Godunov scheme and a relaxed Jacobi-type iteration, respectively. The geometry-based conservative interpolation is employed to remap the solutions from the old mesh to the newly resulting mesh, and a simple slope limiter and a new monitor function are chosen to obtain oscillation-free solutions, and track and resolve both small, local, and large solution gradients automatically. Several numerical experiments are conducted to demonstrate robustness and efficiency of the proposed method. They are a quasi-2D Riemann problem, the double-Mach reflection problem, the forward facing step problem, and two shock wave and bubble interaction problems.     

三维激光烧蚀流体界面不稳定性程序的并行化

在共享存储并行机和MPP并行机上,基于MPI(MessagePassingInterface)并行编程环境,本文研究三维激光烧蚀界而不稳定性程序(Lared-S)的并行实现.三维激光烧蚀的数值模拟采用分裂方法,其90％以上的计算负载存在于流体方程和热传导方程的求解(流体方程的求解采用分裂显格式,热传导方程的求解采用分裂隐格式).本文给出基于三维分裂格式的交替平面数据通信模式.分裂隐格式的求解转化为三对角方程组的求解,其并行实现采用块流水线并行算法.数值实验结果表明交替平面数据通信策略和块流水线并行算法是有效且可扩展的.在共享存储并行机上,应用64台处理机获得93％以上的并行效率;在MPP并行机上,应用128台处理机获得90％以上的并行效率.     

Numerical model of a two-dimensional,non-plane transient magnetohydrodynamic flow

The equations describing two-dimensional three-component magnetohydrodynamic (MHD) transient flows are formulated for a system of spherical coordinates. With the numerical code based on Implicit Continuous Fluid Eulerian (ICE) scheme, MHD flows resulting from a sudden energy release in a stratified medium are examined. Because of the inclusion of out-of-plane components of velocity and magnetic fields, MHD transverse waves are observed in addition to fast, slow and entropy waves. Numerical results for compressible MHD shocks are found in satisfactory agreement with the theoretical predictions.     

Numerical simulation of shock diffraction on unstructured meshes

Shock diffraction over geometric obstacles is performed on two-dimensional unstructured triangular meshes using the AUSM+ flux-vector splitting scheme. Numerical simulations of shock diffraction using structured grids are reviewed in the literature, as are experimental results corresponding to the flow conditions studied. Present unstructured grid results for popular and challenging two-dimensional shock diffraction problems are presented and compared to experimental data and photographs. Benchmark and example test cases were chosen to cover a wide variety of Mach numbers for weak and strong shock waves, and for square and circular geometries. Both single and multiple obstacles are considered, as are obstacles located in the free field and confined in a channel.     

Towards a three-dimensional moving body incompressible flow solver with a linear deformable model

In this study, a three-dimensional fluid–structured parallelized solver is extended from the previous work (Niu et al., 2009 [1]) for moving body simulations. Based on the unified Eulerian and Lagrangian coordinate transformations, the unsteady three-dimensional incompressible Navier–Stokes equations with artificial compressibility (Chorin, 1967 [2]) in a dual-time stepping approach are first derived. To implement unsteady flow calculations, the dual-time stepping strategy including the LU decomposition method is used in the pseudo-time iteration and the second-order accurate backward difference is adopted to discretize the unsteady flow terms. Also, a third-order Roe type flux limited splitting is derived to evaluate the spatial difference of the convective fluxes. The original FORTRAN code is converted to the MPI code and tested on a 64-CPU IBM SP2. The parallel strategy here is based on the partitions of all do-loops in the original FORTRAN code and transferring the calculations inside the do-loop into different CPUs. The partition of the do-loop can be applied on the innermost loop, only or the last two inner loops depending on two-dimensional or three-dimensional problems. This kind of the parallel data partition of the loops is independent of what kind of the explicit or implicit type numerical algorithm used. Therefore, the current parallel approach can take advantage of the MPI language fully to transfer data efficiently among CPUs even for solving the governing equation implicitly. The test results show that a significant reduction of computing time in running the model and a near-linear speed up rate is achieved up to 32 CPUs at IBM SP2. The speed up rate is as high as 31 for using 64 IBM SP2 processors The test shows efficient parallel processing to provide prompt simulation of 3D cavity, unsteady dropping airfoil and blood flows in an aortic tube with a linear elastic modeling of wall motion is included here.