Space-time discontinuous Galerkin finite element method for inviscid gas dynamics

Abstract

This chapter provides an overview of the space-time discontinuous Galerkin finite-element method (DGFEM) for the solution of the Euler equations of gas dynamics. This technique is well-suited for problems that require moving meshes to deal with changes in the domain boundary. The method is demonstrated with the simulation of the elastic deformation of a wing in subsonic and transonic flow. The main features of the space-time discontinuous Galerkin method say that no distinction is made between the space and time variables in the numerical discretization. The space-time DGFEM results in a conservative formulation on deforming meshes, is equivalent to an arbitrary Lagrangian Eulerian formulation, and provides great flexibility in the mesh deformation since the mesh velocity is independent of the fluid particle velocity.