A novel dual reciprocity boundary element formulation for two-dimensional transient convection–diffusion–reaction problems with variable velocity

Abstract

This paper describes a new formulation of the dual reciprocity boundary element method (DRBEM) for two-dimensional transient convection–diffusion–reaction problems with variable velocity. The formulation decomposes the velocity field into an average and a perturbation part, with the latter being treated using a dual reciprocity approximation to convert the domain integrals arising in the boundary element formulation into equivalent boundary integrals. The integral representation formula for the convection–diffusion–reaction problem with variable velocity is obtained from the Green’s second identity, using the fundamental solution of the corresponding steady-state equation with constant coefficients. A finite difference method (FDM) is used to simulate the time evolution procedure for solving the resulting system of equations. Numerical applications are included for three different benchmark examples for which analytical solutions are available, to establish the validity of the proposed approach and to demonstrate its efficiency. Finally, results obtained show that the DRBEM results are in excellent agreement with the analytical solutions and do not present oscillations or damping of the wave front, as it appears in other numerical techniques.