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

TL;DR

This paper develops a high-order discontinuous Galerkin method with curved elements for Euler equations, optimized for GPU implementation to improve boundary resolution and computational efficiency.

Contribution

It introduces a mesh curvature approach based on linear elasticity for high-order boundary approximation in DG methods on GPUs.

Findings

Effective high-order boundary resolution demonstrated

Significant speedup on GPU implementation

Accurate solutions for Euler equations achieved

Abstract

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