ABSTRACT
This chapter discusses some difference methods for the numerical modeling of diffusion processes. Such processes take place, for example, in the propagation of the heat through an isotropic medium at rest, in viscous fluid flows, in flows with chemical reactions, in problems on the propagation of electromagnetic waves, in problems of fluid flows through porous media, etc. The chapter presents a finite volume method for obtaining the difference discretizations of partial differential equations in cases of curvilinear spatial grids. An advantage of the finite volume method is that it is equally well applicable in cases of various spatial irregular grids: the curvilinear grids of quadrilateral cells; the triangular grids; the grids of pentagonal or hexagonal cells; and the grids of Dirichlet cells. The chapter shows how the Mathematica system can be applied for the analysis of the dispersion of difference schemes.
