On the derivation of a boundary element method for diffusion convection-reaction problems of compressible flow in exponentially inhomogeneous media

Abstract

Boundary value problems (BVPs) of anisotropic and exponentially-graded media governed by a diffusion convection-reaction (DCR) equation are considered. The governing equation is of spatially varying coefficients (with an anisotropic diffusion coefficient). The variable coefficients equation is firstly transformed into a constant coefficients equation, from which we derive a boundary integral equation. A boundary element method (BEM) is then constructed to be used for finding numerical solutions to the BVPs. For the computation of the solutions a FORTRAN code is developed. Some examples of problems are solved. The numerical solutions obtained verify the validity of the analysis used to construct the boundary element method with accurate and consistent solutions. The results also show that the BEM procedure elapses very efficient time in producing the solutions. In addition, the results indicate the effect of anisotropy of the media on the solutions.

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.…”