Abstract—

A numerical algorithm is presented for solving the multicomponent gas dynamics equations by the discontinuous Galerkin method on locally adaptive grids. The numerical algorithm uses a data structure and a dynamic local grid adaptation algorithm from the p4est library. We use Lax–Friedrichs–Rusanov and HLLC numerical flows. To get rid of unphysical oscillations, the Barth–Jespersen limiter is applied. As a result of the study, a numerical simulation of the development of the Richtmyer–Meshkov instability (RMI) is performed and the results obtained are compared with the experimental findings and well-known numerical solutions of this problem. It is concluded that the calculated and experimental data are in good agreement. In the future, it is intended to study this process using a model that accounts for the phenomena of viscosity and thermal conductivity.

中文翻译：

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使用不连续伽辽金方法和局部自适应网格对 Richtmyer-Meshkov 不稳定性发展建模

摘要——

提出了一种在局部自适应网格上用非连续伽辽金法求解多组分气体动力学方程的数值算法。数值算法使用来自 p4est 库的数据结构和动态局部网格自适应算法。我们使用 Lax-Friedrichs-Rusanov 和 HLLC 数值流。为了消除非物理振荡，应用了 Barth-Jespersen 限制器。作为研究的结果，对 Richtmyer-Meshkov 不稳定性 (RMI) 的发展进行了数值模拟，并将获得的结果与该问题的实验结果和众所周知的数值解进行比较。得出的结论是，计算和实验数据符合良好。将来，