高精度激波捕捉格式的性能分析

在数值模拟激波-湍流干扰问题时，为了精确模拟湍流脉动的小尺度结构，数值格式应尽量减小自身的数值耗散.但是为了稳定、无震荡地捕捉激波，数值格式又必须具有一定程度的数值耗散.基于上述这2种相互矛盾的要求，采用无黏泰勒格林涡、可压缩湍流等经典算例对目前广受好评的几种高精度格式进行了系统地对比.一系列的计算分析表明，当前工程中广泛应用的高精度格式虽然都能一定程度地满足上述2种要求，但与理想目标仍有较大的差距.

Assessment of shock capturing methods for numerical simulations of compressible turbulence with shock waves

The direct numerical simulation (DNS) and large eddy simulation (LES) of turbulent flows raise challenges to the numerical schemes, especially when they are combined with shock waves. The two demands of the schemes seem to be contrary: the simulation of small turbulence scales requires non-dissipative schemes while the capture of shock waves requires dissipative schemes. To have a systematic comparison of some popular schemes' properties in solving the problems above, a suite of test cases were displayed,Taylor-Green vortex, Shu-Osher problem, and compressible isotropic turbulence. Through systematic analysis and comparisons, results show that the widely used high order schemes are capable of satisfying the two demands required above in some extent. However, both of them have their advantages and disadvantages compared to each other and no one can be called perfect. Thus, they are still far from the theoretic object, and their improvements are in high demands.