Modeling of Richtmyer–Meshkov instability development using the discontinuous Galerkin method and local-adaptive meshes

The article presents a numerical algorithm for solving equations of multicomponent gas dynamics using the discontinuous Galerkin method on local-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 numerical and HLLC flows. To get rid of non-physical oscillations, the Barth–Jespersen limiter is applied. As a result of the study, a numerical simulation of the development of the Richtmyer–Meshkov instability was carried out, the results obtained were compared with experimental results and known numerical solutions of this problem. It is concluded that the calculated and experimental data are in good agreement. In the future, it is expected to study this process using a model that takes into account the phenomena of viscosity and thermal conductivity.