An arbitrary Lagrangian-Eulerian RKDG method for compressible Euler equations on unstructured meshes: Single-material flow

In this paper, we present a high-order arbitrary Lagrangian Eulerian (ALE) method for compressible single-material flow on adaptive moving unstructured meshes. The discretization of system is implemented by Runge-Kutta Discontinuous Galerkin (RKDG) method. The vertex velocity is given by the approach of mesh movement from G. Chen et al. (2008) [8] . The new mesh can be automatically redistributed and concentrated on the regions with large gradient value of the variables. A HWENO reconstruction is used to eliminate false oscillations which maintains compactness of DG methods. In addition, we prove the property that the material derivatives of the Lagrangian basis functions are equal to zero with which the scheme is shown to satisfy the geometric conservation law (GCL). Furthermore, the scheme is conservative for mass, momentum and total energy. Numerical examples are presented to illustrate the good performance and high-order accuracy of the scheme.