High-Order ALE Multi-Material Hydrodynamics

A high-order discontinuous Galerkin (DG) arbitrary Lagrangian-Eulerian (ALE) method for hyperbolic PDEs with non-conservative products is presented. This method is applied to the pressure-temperature non-equilibrium multi-material hydrodynamics equations. This system allows multiple materials to simultaneously possess different thermodynamic states at a given spatial location, leading to a more physically accurate picture than the alternative. A direct ALE strategy is utilized for mesh motion, thereby allowing the use of high-order time integration schemes. It is coupled with an algebraic interface reconstruction technique (THINC) for resolving material interfaces. Using standard tests, it is confirmed that the DG-ALE method is geometric conservation law (GCL) preserving and well-balanced. Further tests demonstrating preliminary multi-material capabilities of the ALE method are also shown.