The boundary element method applied to the solution of two-dimensional diffusion–advection problems for non-isotropic materials

Abstract

A boundary element method (BEM) formulation is developed for the analysis, in the time-domain, of the diffusion–advection problem for non-isotropic materials in two dimensions. As the diffusion–advection equation describes, among others, the pollution dispersion problem, the development of formulations capable of dealing with this social and environmental problem is always welcome. The formulation presented here employs the fundamental solution of the steady-state pure diffusion problem. Therefore, the resulting BEM equation presents three domain integrals, related to the velocity components, to the decay term, and to the time-derivative of the variable of interest. This time-derivative is approximated by means of a backward finite difference scheme. Three examples are presented and discussed at the end of the article. The first example shows how varying the value of the diffusion coefficient in one direction, while keeping a constant value in the other direction, influences the results in a pure diffusion problem. The second example deals with a pollutant dispersion problem, and consequently, is described by the diffusion–advection equation. The third example also deals with a pollutant dispersion problem, but the analysis is carried out in a linear channel with a variable width.