Multi-material ALE methods in unstructured grids

Arbitrary Lagrangian Eulerian (ALE) methods have existed for several decades. However, three-dimensional Multi-Material Arbitrary Lagrangian Eulerian (MMALE) methods for unstructured grids are relatively new. MMALE algorithms provide the framework to model sections of a simulation as either Lagrangian, ALE, or Eulerian. In addition, sections of a simulation can switch in time between mesh motions as the distortion of the problem dictates. The MMALE method provides the accuracy of Lagrangian mesh motion and the robustness of Eulerian mesh motion within the same framework. Extending this method to unstructured grids allows for more accurate representation of curved surfaces and complex geometries. This paper examines the algorithms required for the MMALE method and the extensions to these algorithms for unstructured meshes. In addition, second-order behavior of the MMALE algorithm as it exists in the high energy density physics code Arbitrary Lagrangian Eulerian General Research Applications code (ALEGRA) is demonstrated, along with a practical example of its usefulness.