Developement of multigrid methods for convergence acceleration of solvers for Navier-Stokes equations on non-structured meshes

The objective of the study is to develop an algorithm for automatic directional coarsening of anisotropic meshes based on the finest level mesh to provide coarser meshes for geometric multigrid. Characteristic parameters of the meshes are high aspect ratio (of order 10 near the profile). The meshes are assumed to have a layer structure in boundary-layer zones. The aim of the study is to design a mesh-coarsening algorithm such that the resulting meshes, coarsened by a given coarsening factor, respect the layer structure in boundary layers and give pertinent coarse meshes for geometric multigrid. This work can be viewed as a continuation of [3, 4], which design efficient automatic meshcoarsening algorithms for isotropic meshes in 2D and 3D. The major goal of the anisotropic coarsening process is to coarsen boundary layer zones on the fine mesh, while preserving their layer structure and respecting a prescribed maximal coarsening factor (usually 2). In this respect, we have chosen to proceed with the coarsening process by layers, starting at the profile boundary. The whole algorithm could be summarized as follows: