Reconstructed discontinuous galerkin methods for compressible flows in ALE formulation

A high-order reconstructed discontinuous Galerkin (rDG) method in arbitrary Lagrangian-Eulerian (ALE) formulation is proposed in this paper, for moving and deforming domain problems. The Taylor basis functions defined on the time-dependent moving domain are used for the rDG method. This will require additional considerations in the derived equations as well as the Geometric Conservation Law (GCL). Following the method in the literature, we enforce the GCL condition by modifying the grid velocity terms on the right-hand side of the discretized equations. The unstructured curved grids are considered in this work and the radial basis function (RBF) interpolation method is responsible for the mesh movement. To achieve high order accuracy in time, the third order ESDIRK3 scheme is used for the temporal integration. To demonstrate the spatial and temporal order of accuracy, and to show the ability of handling moving boundary problems, several numerical examples are conducted using the rDG-ALE method.