A Provably Stable Discontinuous Galerkin Spectral Element Approximation for Moving Hexahedral Meshes
Abstract
We design a novel provably stable discontinuous Galerkin spectral element (DGSEM) approximation to solve systems of conservation laws on moving domains. To incorporate the motion of the domain, we use an arbitrary Lagrangian-Eulerian formulation to map the governing equations to a fixed reference domain. The approximation is made stable by a discretization of a skew-symmetric formulation of the problem. We prove that the discrete approximation is stable, conservative and, for constant coefficient problems, maintains the free-stream preservation property. We also provide details on how to add the new skew-symmetric ALE approximation to an existing discontinuous Galerkin spectral element code. Lastly, we provide numerical support of the theoretical results.
Keywords
Cite
@article{arxiv.1510.09011,
title = {A Provably Stable Discontinuous Galerkin Spectral Element Approximation for Moving Hexahedral Meshes},
author = {David A. Kopriva and Andrew R. Winters and Marvin Bohm and Gregor J. Gassner},
journal= {arXiv preprint arXiv:1510.09011},
year = {2015}
}