Optimization-Based Reference-Matrix Rezone Strategies for Arbitrary Lagrangian-Eulerian Methods on Unstructured Meshes

Mikhail Shashkov, Patrick Knupp


The objective of the Arbitrary Lagrangian-Eulerian (ALE) methodology for solving multidimensional fluid flow problems is to move the computational mesh, using the flow as a guide, to improve the robustness, accuracy and efficiency of the simulation. A principal element is the rezone phase in which the computational ("rezoned") mesh is created that is adapted to the fluid motion. Here we describe a general rezone strategy that ensures the geometric quality of the computational mesh, while keeping it as close as possible to the Lagrangian mesh. In terminology of mesh generation community our method can be classified as a two-stage smoothing algorithm. We provide numerical examples to demonstrate the robustness and the effectiveness of our methodology.


ALE; rezoning; optimization; reference Jacobian; condition number.

Full Text: