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首页> 外文期刊>International Journal for Numerical Methods in Fluids >A matrix-free high-order discontinuous Galerkin compressible Navier-Stokes solver: A performance comparison of compressible and incompressible formulations for turbulent incompressible flows
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A matrix-free high-order discontinuous Galerkin compressible Navier-Stokes solver: A performance comparison of compressible and incompressible formulations for turbulent incompressible flows

机译：无矩阵的高阶空白不连续Galerkin可压缩Navier-Stokes求解器：湍流不可压缩流动的可压缩和不可压缩配方的性能比较

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摘要

Both compressible and incompressible Navier-Stokes solvers can be used and are used to solve incompressible turbulent flow problems. In the compressible case, the Mach number is then considered as a solver parameter that is set to a small value, M approximate to 0.1, in order to mimic incompressible flows. This strategy is widely used for high-order discontinuous Galerkin (DG) discretizations of the compressible Navier-Stokes equations. The present work raises the question regarding the computational efficiency of compressible DG solvers as compared to an incompressible formulation. Our contributions to the state of the art are twofold: Firstly, we present a high-performance DG solver for the compressible Navier-Stokes equations based on a highly efficient matrix-free implementation that targets modern cache-based multicore architectures with Flop/Byte ratios significantly larger than 1. The performance results presented in this work focus on the node-level performance, and our results suggest that there is great potential for further performance improvements for current state-of-the-art DG implementations of the compressible Navier-Stokes equations. Secondly, this compressible Navier-Stokes solver is put into perspective by comparing it to an incompressible DG solver that uses the same matrix-free implementation. We discuss algorithmic differences between both solution strategies and present an in-depth numerical investigation of the performance. The considered benchmark test cases are the three-dimensional Taylor-Green vortex problem as a representative of transitional flows and the turbulent channel flow problem as a representative of wall-bounded turbulent flows. The results indicate a clear performance advantage of the incompressible formulation over the compressible one.
机译：可以使用可压缩和不可压缩的Navier-Stokes溶剂，并用于解决不可压缩的湍流流动问题。在可压缩的情况下，马赫数被认为是设置为小值的求解器参数，M近似为0.1，以模仿不可压缩的流动。该策略广泛用于可压缩Navier-Stokes方程的高阶不连续的Galerkin（DG）离散化。与不可压缩的制剂相比，本作对可压缩DG溶剂的计算效率提出了问题。我们对本领域状态的贡献是双重的：首先，我们基于高效的矩阵实现，为可压缩Navier-Stokes方程提供了一种高性能的DG求解器，该实现是针对具有翻转/字节比率的现代缓存的多核架构显着大于1.本工作中提出的性能结果侧重于节点级性能，我们的结果表明，对压缩Navier-Stokes的当前最先进的DG实现有很大的性能改进潜力方程式。其次，这种可压缩的Navier-Stokes求解器通过将其与使用相同的矩阵实现的不可压缩的DG求解器进行比较来透视。我们讨论了解决方案策略之间的算法差异，并对性能进行了深入的数值调查。考虑的基准测试用例是三维泰勒 - 绿色涡流问题，作为过渡流的代表和湍流通道流问题作为壁限湍流流动的代表。结果表明可压缩剂上不可压缩配方的明显性能优势。

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