Abstract

Euler equations for multidimensional inviscid gas flows with multispecies and multi‑reaction are considered. By using the Marchuk–Strang splitting method, an implicit numerical scheme for this system is constructed. Its convection part is computed using the bicompact scheme SDIRK3B4 of fourth order in space and third order in time, while its chemical part is computed using the L-stable Runge–Kutta method of second order. The SDIRK3B4 scheme is compared with the WENO5/SR scheme in the case of one- and two-dimensional flows with detonation waves. It is shown that the SDIRK3B4 scheme has the same actual accuracy as the WENO5/SR, but the former needs fewer time steps by a factor of 20–40 and does not require any special algorithms to suppress the nonphysical breakdown of detonation waves on relatively coarse meshes.

中文翻译：

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多物种多反应气流数值建模的高阶双紧方案

摘要

考虑具有多物种和多反应的多维无粘性气体流的欧拉方程。通过使用Marchuk–Strang拆分方法，为该系统构造了一个隐式数值方案。它的对流部分是使用时域四阶，时间上是三阶的双紧缩方案SDIRK3B4计算的，而其化学部分是使用L计算的-stable稳定的Runge–Kutta方法。在带有爆轰波的一维和二维流的情况下，将SDIRK3B4方案与WENO5 / SR方案进行比较。结果表明，SDIRK3B4方案具有与WENO5 / SR相同的实际精度，但是前者所需的时间步长减少了20-40倍，并且不需要任何特殊的算法来抑制相对较粗的爆轰波的非物理击穿。网格。