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 CVTmesh 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.