Radial integration boundary element method for solving two-dimensional unsteady convection–diffusion problem

Abstract

Numerical solution of two-dimensional unsteady convection–diffusion problem is carried out by using the radial integration boundary element method in the paper. A boundary domain integral equation is established for the purpose by using the fundamental solution of Laplace equation. The convective and time-dependent terms of governing equation lead to the appearance of two domain integrals including the unknown quantities in the integral equation. The radial integration method is used to transform the two domain integrals into the equivalent boundary integrals over the global boundary by approximating the unknown quantities through the augmented fourth-order spline radial basis function. Thus, a pure boundary element algorithm with the requirement of boundary-only discretization and some internal points instead of internal cells is developed. The finite difference scheme for discretizing the time-dependent term is utilized to assemble the final system of equations. Several numerical examples are given to illustrate the accuracy and efficiency of the proposed method.