A high‐order Runge‐Kutta discontinuous Galerkin method with a subcell limiter on adaptive unstructured grids for two‐dimensional compressible inviscid flows

Abstract

SummaryA robust, adaptive unstructured mesh refinement strategy for high‐order Runge‐Kutta discontinuous Galerkin method is proposed. The present work mainly focuses on accurate capturing of sharp gradient flow features like strong shocks in the simulations of two‐dimensional inviscid compressible flows. A posteriori finite volume subcell limiter is employed in the shock‐affected cells to control numerical spurious oscillations. An efficient cell‐by‐cell adaptive mesh refinement is implemented to increase the resolution of our simulations. This strategy enables to capture strong shocks without much numerical dissipation. A wide range of challenging test cases is considered to demonstrate the efficiency of the present adaptive numerical strategy for solving inviscid compressible flow problems having strong shocks.