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In this work we consider Runge-Kutta discontinuous Galerkin methods (RKDG)for the solution of hyperbolic equations enabling high order discretization inspace and time. We aim at an efficient implementation of DG for Euler equationson GPUs. A mesh curvature approach is presented for the proper resolution ofthe domain boundary. This approach is based on the linear elasticity equationsand enables a boundary approximation with arbitrary, high order. In order todemonstrate the performance of the boundary curvature a massively parallelsolver on graphics processors is implemented and utilized for the solution ofthe Euler equations of gas-dynamics.

A curved-element unstructured discontinuous Galerkin method on GPUs for the Euler equations