A boundary element method for anisotropic-diffusion convection-reaction equation in quadratically graded media of incompressible flow

Abstract

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

“…Rap et al [23], Ravnik and Škerget [25,26], Li et al [18] and Pettres and Lacerda [22] considered the case of isotropic diffusion and variable coefficients (inhomogeneous media). Recently Azis and co-workers had been working on steady state problems of anisotropic inhomogeneous media for several types of governing equations, for examples [5,32] for the modified Helmholtz equation, [4,14,24,30,27,11,17] for the diffusion convection reaction equation, [29,8,13,16] for the Laplace type equation, [10,2,20,21,15] for the Helmholtz equation.…”