A meshless geometric multigrid method for a grid with a high aspect ratio

In this paper, a new semi-coarsening method is proposed by extending the meshless geometric multigrid method based on full-coarsening for an anisotropic unstructured mesh. The present semi-coarsening method is based on the distance weighting for a finite volume grid and validated by solving the pressure equation of CUPID, which is a CFD code with an unstructured grid. Although the present semi-coarsening method requires more coarsening steps than the full-coarsening method to build the coarsest grid, the numbers of V-cycles required to the convergence are nearly the same for the two methods. Therefore, the proposed semi-coarsening method is found to perform much better than the conventional full-coarsening method when an unstructured grid with a high aspect ratio is involved in the V-cycle multi-grid computation. Furthermore, the present method works well with a hybrid mesh, where brick elements with high aspect ratios near the wall boundary are coupled with isotropic tetrahedrons.