Application of computational algorithms with higher order of accuracy to the modeling of two-dimensional problems on development of hydrodynamic instability

{This article examines application of computational algorithms with an increased order of accuracy for modeling two-dimensional problems of development of hydrodynamic instabilities. The efficiency of using algorithms to improve the accuracy and reliability of modeling in this area is considered. More specifically, the paper describes a numerical algorithm for solving the problem of development of Richtmayer-Meshkov instability. To construct the algorithm, the authors use the WENO scheme of the fifth order of accuracy Several problems are solved numerically using the developed method. The article models such processes as flows at a time of 4 046 microseconds, a change in the width of the region filled with sulfur hexafluoride, numerical schlieren patterns at a time of 877 microseconds, a change in the width of the region filled with heavy gas. The results are obtained by various methods on grids of different dimensions and compared with experimental data. It is shown that schemes with WENO reconstruction of the 5th order of accuracy demonstrate results closer to full-scale experiments.