Solution of two-dimensional diffusion–advection problems for non-isotropic media with spatially variable velocity field by the boundary element method

Abstract

This work presents a boundary element method formulation for the solution of the diffusion–advection problem. The formulation, developed for two-dimensional problems, for non-isotropic media, considers a spatially variable velocity field. The only way to deal with such a kind of problem is employing a steady-state fundamental solution. Consequently, the basic BEM equation presents one domain integral related to the velocity components, and another one related to the time derivative of the variable of interest, which is approximated using a backward finite difference scheme. BEM results are compared with an available analytical solution in the first part of the first example, and with the results provided by a finite element method formulation, taken as reference ones, in the second part of the first example and in the second example. From the comparisons, one can observe a good agreement between the results furnished by the proposed formulation and the analytical and reference solutions.