Transient Convection-Diffusion-Reaction Problems with Variable Velocity Field by Means of DRBEM with Different Radial Basis Functions

Abstract

This work describes a novel numerical formulation of the dual reciprocity boundary element method (DRBEM) for two-dimensional transient convection-diffusion-reaction problems with variable velocity. Firstly, the formulation splits the velocity field into an average (constant) and a perturbation (variable) 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 Green’s second identity, using the fundamental solution of the corresponding steady-state equation with constant coefficients. Another objective is to discuss the treatment of the convective terms, which involve gradients of the problem variable, and their modelling using DRM. A finite difference method (FDM) is used to simulate the time evolution procedure for solving the resulting system of equations. Numerical experiments are included for two different problems for which analytical solutions are available, to establish the validity of the proposed approach and to demonstrate the efficiency of the proposed technique. Finally, the results obtained show an excellent agreement with the analytical solutions and do not show oscillations or damping of the wave front, as appear in other numerical techniques.