Using the feasible set method for rezoning in ALE

One of the steps in the Arbitrary Lagrangian Eulerian (ALE) algorithm is the improvement of the quality of the computational mesh. This step, commonly referred to as rezoning, is essential for maintaining a mesh that does not become invalid during a simulation. In this paper, we present a new robust and computationally efficient 2D mesh relaxation method. This feasible set method is a geometric method for finding the convex polygon that represents the region of coordinates that a vertex in a mesh can occupy while the mesh around it remains valid. After the feasible set has been computed for a vertex in a mesh, a new vertex location can be chosen that lies inside this feasible set. As a result, the mesh after relaxation is guaranteed to be valid. We present an example ALE simulation, that highlights the robustness of the feasible set method when used as a rezoning method in ALE.