Diffusion convection-reaction equation in exponentially graded media of incompressible flow: Boundary element method solutions

Abstract

We setup boundary value problems (BVPs) for exponentially graded media. The BVPs are governed by a diffusion convection-reaction (DCR) equation of spatially varying coefficients (with an anisotropic diffusion coefficient). A boundary element method (BEM) is utilized to find numerical solutions to BVPs. The numerical solutions obtained verify the validity of the analysis used to derive the BEM with accurate and consistent solutions. The computation shows that the BEM procedure elapses very efficient time in producing the solutions. In addition, the results show the effect of anisotropy and inhomogeneity of the media on the solutions. To illustrate the application, an example of a layered material is presented.