Radial integration boundary element method for two-dimensional non-homogeneous convection-diffusion-reaction problems with variable source term

This paper describes a new formulation of the radial integration boundary element method (RIBEM) for two-dimensional non-homogeneous convection-diffusion-reaction problems with variable source terms. The radial integration method (RIM) is implemented to transform the resulting domain integral into equivalent boundary integrals, and thus a boundary-only integral equation formulation can be achieved. The fundamental solution of the steady-state convection-diffusion-reaction equation with constant coefficients is employed. The integral representation formula for the convection-diffusion-reaction problem with source term is obtained from Green's second identity. Numerical applications are included for five different cases, for which analytical solutions are available, to establish the validity of the proposed approach and to demonstrate convergence and efficiency of the proposed technique. Results obtained show that the RIBEM produced an excellent agreement with the analytical solutions and the results do not present oscillations or damping of the wave front, as may appear in other numerical techniques.