Discontinuous Galerkin spectral element approximations on moving meshes

作者：Minoli Cesar A Acosta; Kopriva David A^*

来源：Journal of Computational Physics, 2011, 230(5): 1876-1902.

DOI：10.1016/j.jcp.2010.11.038

• Discontinuous Galerkin Spectral Element Method DGSEM
• Moving mesh
• Arbitrary Lagrangian-Eulerian ALE
• Discrete Geometric Conservation Law (DGCL)

We derive and evaluate high order space Arbitrary Lagrangian-Eulerian (ALE) methods to compute conservation laws on moving meshes to the same time order as on a static mesh. We use a Discontinuous Galerkin Spectral Element Method (DGSEM) in space, and one of a family of explicit time integrators such as Adams-Bashforth or low storage explicit Runge-Kutta. The approximations preserve the discrete metric identities and the Discrete Geometric Conservation Law (DGCL) by construction. We present time-step refinement studies with moving meshes to validate the approximations. The test problems include propagation of an electromagnetic gaussian plane wave, a cylindrical pressure wave propagating in a subsonic flow, and a vortex convecting in a uniform inviscid subsonic flow. Each problem is computed on a time-deforming mesh with three methods used to calculate the mesh velocities: from exact differentiation, from the integration of an acceleration equation, and from numerical differentiation of the mesh position.

• 出版日期2011-3-1