The Ball-Vertex Method: a New Simple Spring Analogy Method for Unstructured Dynamic Meshes

We study the problem of deforming unstructured grids using pseudo-structural lumped-parameter systems. A basic network of edge springs is complemented with an additional set of linear springs that oppose element collapsing. This is here achieved by confining each mesh vertex to its ball, through linear springs that are attached to the vertex and to its projections on the ball entities. The resulting linear pseudo-structural problem can be solved efficiently with an iterative method. The proposed procedures are compared with a revisited version of the torsional spring method with the help of two and three-dimensional example problems.