Numerical Methods for Quantity Remapping in the Context of Indirect Arbitrary Lagrangian-Eulerian (ALE) Hydrodynamics

Abstract

For hydrodynamic simulations of fast flows, the indirect Arbitrary Lagrangian Eulerian (ALE) methods represent one of the few state of the art numerical approaches, which are efficient, accurate, and robust enough for realistic calculations. In this approach, a Lagrangian solver is used to advance the solution along with the computational mesh in time, while its robustness is achieved by smoothing (regularization) of the mesh. Remapping is one of the essential parts of the ALE algorithm, conservatively interpolating the fluid quantities between different computational meshes. This habilitation thesis summarizes the contribution of the author in the field of remapping methods. After a brief description of the ALE algorithm, it focuses on the description of the remapping approaches and emphasizes the input of the author in the form of his commented articles. It mainly includes his work related to a combination of intersection- and sweptbased remapping approaches, the remap in multi-material problems, and the development of compatible algorithms for the remap of all fluid quantities. Finally, several applications are presented, especially from the field of hydrodynamic laserplasma simulations.