Finite-difference Approximation of Mathematical Physics Problems on Irregular Grids

Abstract

Mathematical physics problems are often formulated by means of the vector analysis diïrential operators: divergence, gradient and rotor. For approximate solutions of such problems it is natural to use the corresponding operator statements for the grid problems, i.e., to use the so-called VAGO (Vector Analys Grid Operators) method. In this paper, we discuss the possibilities of such an approach in using general irregular grids. The vector analysis difference operators are constructed using the Delaunay triangulation and the Voronoi diagrams. The truncation error and the consistency property of the difference operators constructed on two types of grids are investigated. Construction and analysis of the difference schemes of the VAGO method for applied problems are illustrated by the examples of stationary and non-stationary convection-diffusion problems. The other examples concerned the solution of the non-stationary vector problems described by the second-order equations or the systems of first-order equations. © 2005, Institute of Mathematics, NAS of Belarus. All rights reserved.