A high-order discontinuous Galerkin method with unstructured space–time meshes for two-dimensional compressible flows on domains with large deformations. (2nd September 2015) - Wang, Luming; Persson, Per-Olof
Highlights: A high-order discontinuous Galerkin method for fully unstructured space–time meshes. Force-based iterative method with connectivity updates for the moving meshes. An efficient algorithm for conforming tetrahedral space–time mesh generation. Applications to compressible flows with large complex domain deformations. Abstract: We present a high-order accurate space–time discontinuous Galerkin method for solving two-dimensional compressible flow problems on fully unstructured space–time meshes. The discretization is based on a nodal formulation, with appropriate numerical fluxes for the first and the second-order terms, respectively. The scheme is implicit, and we solve the resulting non-linear systems using a parallel Newton–Krylov solver. The meshes are produced by a mesh moving technique with element connectivity updates, and the corresponding space–time elements are produced directly based on these local operations. To obtain globally conforming tetrahedral meshes, we first derive the required conditions on a prism boundary mesh to allow for a valid local triangulation. Next, we present an efficient algorithm for finding a global mesh that satisfies these conditions. We also show how to add and remove mesh nodes, again using local constructs for the space–time mesh. Our method is demonstrated on a number of test problems, showing the high-order accuracy for model problems, and the ability to solve flow problems on domains with complex large deformations.