A coupled ALE-AMR method for shock hydrodynamics

We present a numerical method combining adaptive mesh refinement (AMR) with arbitrary Lagrangian-Eulerian (ALE) mesh motion for the simulation of shock hydrodynamics on unstructured grids. The primary goal of the coupled method is to use AMR to reduce numerical error in ALE simulations at reduced computational expense relative to uniform fine mesh calculations, in the same manner that AMR has been used in Eulerian simulations. We also identify deficiencies with ALE methods that AMR is able to mitigate, and discuss the unique coupling challenges. The coupled method is demonstrated using three-dimensional unstructured meshes of up to O(107) tetrahedral cells. Convergence of ALE-AMR solutions towards both uniform fine mesh ALE results and analytic solutions is demonstrated. Speed-ups of 5-10 ×  for a given level of error are observed relative to uniform fine mesh calculations.