Application of discontinuous Galerkin method to modeling of two-dimensional flows of a multicomponent ideal gases mixture using local adaptive mesh refinement

In this article a numerical algorithm is developed for solving of gas dynamics equations for a mixture of ideal gases on adaptive locally refined grids. The algorithm is based on discontinuous Galerkin method. To avoid the appearance of non-physical oscillations near the discontinuities, the Barth-Jespersen limiter is used. The numerical algorithm is based on the data structure and algorithms of the p4est library. In present work the numerical simulation of one problem of Richtmyer-Meshkov instability development is considered and the triple point problem is solved using the developed numerical algorithm of high accuracy order. The obtained results are in good agreement with the well-known numerical solutions. The pictures plotted basing on the solution describe in detail the dynamics of the complex flows under consideration.