An integral equation approach to the unsteady convection–diffusion equations

Abstract

An integral equation approach is proposed to solve the unsteady convection–diffusion equations. In this approach, the second order Adams–Moulton method is firstly utilized for the time discretization. Then by using the Green's function of the Laplace equation in the series form, the convection–diffusion equation is transformed into an integral equation that is further converted into an algebraic equation system. The accuracy, convergence and the stability of this integral equation approach are examined by four examples. In comparison with the characteristic variational multiscale method and the finite volume element method, the integral equation approach shows a higher accuracy. Compared with the finite volume element method the integral equation approach has a better convergence. In solving the convection dominated convection–diffusion problems the integral equation approach demonstrates a good stability.