An adaptive mesh refinement in the finite volume method

Abstract

In this paper we describe the method of adaptive mesh refinement, based on the estimation of eigenvalues of discretization matrix. This estimation based on Gershgorin Circle Theorem. This method can be used for unstructured meshes in two-dimensional problems as well as and in three-dimensional. The implementation of the grid adaptation algorithm was made within OpenFOAM open source library of continuum mechanics. This library consists of a set of modules for computational needs, modules written in C++. We give two numerical examples, which show the effectiveness of the proposed method of mesh adaptation.