Numerical solutions for anisotropic-diffusion convection problems of incompressible flow in exponentially graded media

Abstract

A boundary element method is utilized to find numerical solutions to boundary value problems of exponentially graded media governed by a spatially varying coefficients anisotropic-diffusion convection equation. The variable coefficients equation is firstly transformed into a constant coefficients equation for which a boundary integral equation can be formulated. A boundary element method (BEM) is then derived from the boundary integral equation. Some problems are considered. The numerical solutions justify the validity of the analysis used to derive the boundary element method with accurate and consistent solutions. A FORTRAN script is developed for the computation of the solutions. The computation shows that the BEM procedure elapses very efficient time in producing the solutions. In addition, results obtained from the considered examples show the effect of the anisotropy of the media on the solutions. An example of a layered material is presented as an illustration of the application.

Numerical Simulation for Unsteady Anisotropic-Diffusion Convection Equation of Spatially Variable Coefficients and Incompressible Flow

“…The equation considered is almost similar to equation (1.1) but with limitation d 11 ̸ = d 22 , d 12 = 0. This paper is intended to extend the recently published works on anisotropic diffusion convection equation with variable coefficients [31,6,9,28,1] from the steady state to unsteady state equation.…”