Numerical solution to diffusion convection-reaction equation with trigonometrically variable coefficients of incompressible flow

Abstract

This paper is concerned with finding numerical solutions to boundary value problems (BVPs) governed by a diffusion convection-reaction (DCR) equation of in-spatial-trigonometrically varying coefficients with an anisotropic diffusion coefficient. The variable coefficients equation is firstly transformed into a constant coefficients equation. A boundary integral equation is the derived from the constant coefficients equation. Consequently, a boundary element method (BEM) is developed and utilized to find numerical solutions to the boundary value problems. For the computation of the solutions for some examples of problems, a FORTRAN script is constructed. The numerical solutions obtained verify the validity of the analysis used to derive the BEM. The results also show that the BEM procedure elapses very efficient time in producing very accurate and consistent solutions. Moreover, the results indicate the effect of anisotropy and inhomogeneity of the media on the solutions.