A Runge Kutta Discontinuous Galerkin Method for Lagrangian Compressible Euler Equations in Two-Dimensions (Communications in Computational Physics, 2020)
This paper presents a new Lagrangian type scheme for solving the Eulerequations of compressible gas dynamics. In this new scheme the system of equationsis discretized by Runge-Kutta Discontinuous Galerkin (RKDG) method, and the meshmoves with the fluid flow. The scheme is conservative for the mass, momentum andtotal energy and maintains second-order accuracy. The scheme avoids solving the geometricalpart and has free parameters. Results of some numerical tests are presentedto demonstrate the accuracy and the non-oscillatory property of the scheme.