A Discontinuous Galerkin Method for the Navier-Stokes Equations on Deforming Domains using Unstructured Moving Space-Time Meshes

We describe a high-order accurate space-time discontinuous Galerkin (DG) method for solving compressible flow problems on two-dimensional moving domains with large deformations. The DG discretization and space-time numerical fluxes are formulated on a three-dimensional space-time domain. The scheme is implicit, and we solve the resulting non-linear systems using a parallel Newton-Krylov solver. Instead of remeshing when the mesh elements are deformed, we use local mesh operations such as node movement and edge flips to improve the mesh at each time step. We then produce a globally conforming space-time mesh using an efficient algorithm based on element extrusions between two consecutive spatial meshes. In this way, no additional nodes are inserted for each spacetime mesh slab except for those on the spatial meshes. We show various numerical examples with complex domain deformations to illustrate both the accuracy and the capabilities of our method.