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Simulations of Compressible Taylor-Green Flow by a Discontinuous Galerkin Method

机译：不连续Galerkin方法模拟可压缩的泰勒格林流

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A high-order discontinuous Galerkin method is applied to the compressible Taylor-Green vortex at Mach 0.1 to evaluate the method, and to investigate alternative means of evaluating solution accuracy when an exact solution is not available. Two distinct variants of the viscous terms produced nearly identical results, which is consistent with the convection dominant nature of the flow. Grid refinements on hexahedral grids were performed to an effective grid resolution of 1042~3 degrees of freedom. Error analysis using norms of the change in the solution between grid refinements indicate that the solution is entering an asymptotic regime at an effective grid resolution of ≈369~3 degrees of freedom. Simulations on tetrahedral grids produced similar or better results, in particular, converging to peak enstrophy on much coarser grids. These well-resolved results indicate that the compressible solution is measurably different from the incompressible case, and that the incompressible case cannot be used to quantitatively evaluate the accuracy of a high-order method. Further, a volume-averaged quantity hides much of the details of the flow and is not a suitable metric for evaluating a high-order method. Norms based on direct comparison of a sampling of field values between successive grids provides a reliable measure of error convergence.
机译：在不可用精确解的情况下，将高阶不连续Galerkin方法应用于可压缩的Taylor-Green涡旋（速度为0.1马赫），以评估该方法，并研究评估解精度的其他方法。粘性项的两个截然不同的变体产生了几乎相同的结果，这与流动的对流支配性是一致的。在六面体网格上进行网格细化，以达到1042〜3自由度的有效网格分辨率。使用网格细化之间的解决方案变化的范数进行的误差分析表明，该解决方案正在以大约369〜3自由度的有效网格分辨率进入渐近状态。在四面体网格上的模拟产生了相似或更好的结果，特别是在更粗糙的网格上收敛到峰值涡旋。这些良好解决的结果表明，可压缩溶液与不可压缩情况有明显不同，并且不可压缩情况不能用于定量评估高阶方法的准确性。此外，体积平均数量隐藏了很多流程细节，而不是用于评估高阶方法的合适度量。基于连续网格之间场值采样的直接比较的规范提供了误差收敛的可靠度量。

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