Moving Meshes to Fit Large Deformations Based on Centroidal Voronoi Tessellation (CVT)

Abstract

The essential criterion for stability and fast convergence of CFD-solvers (CFD - computational fluid dynamics) is a good quality of the mesh. Based on results of [30] in this paper we use the so-called centroidal Voronoi tessellation (CVT) not only for mesh generation and optimization. The CVT is applied to develop a new mesh motion method. The CVT provides an optimal distribution of generating points with respect to a cell density function. For a uniform cell density function the CVT results in high-quality isotropic meshes. The non-uniform cases lead to a trade-off between isotropy and fulfilling cell density function constraints. The idea of the proposed approach is to start with the CVT-mesh and apply for each time step of transient simulation the so-called Lloyd’s method in order to correct the mesh as a response to the boundary motion. This leads to the motion of the whole mesh as a reaction to movement. Furthermore, each step of Lloyd’s method provides a further optimization of the underlying mesh, thus the mesh remains close to the CVT-mesh. Experience has shown that it is usually sufficient to apply a few iterations of the Lloyd’s method per time step in order to achieve high-quality meshes during the whole transient simulation. In comparison to previous methods our method provides high-quality and nearly isotropic meshes even for large deformations of computational domains.