New Mesh Motion Solver for Large Deformations based on CVT

The essential criterion for stability and fast convergence of CFD-solvers is a good quality of the mesh. In this paper, the so-called centroidal Voronoi tessellation (CVT) is applied to develop a new mesh motion method. Up to now the CVT has been used primarily for mesh generation and optimization. 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. A major advantage of the proposed method is that the interpolation of underlying fields for the cell centres is not required, because the number of cells and field affiliation to these cells remains unchanged. In comparison to previous methods our method provides high-quality and nearly isotropic meshes even for large deformations of the computational domain.