Radial integration BEM for steady convection-conduction problem with spatially variable velocity and thermal conductivity

In this paper, the radial integration boundary element method without internal cells is presented for solving steady convection-conduction problem with spatially variable velocity and thermal conductivity. The temperature boundary integral equation is derived by employing the fundamental solution for the potential problem (Green function) as well as the normalized temperature and thermal conductivity, which results in the appearance of domain integrals including the unknown temperature. To avoid evaluating the domain integrals with the use of internal cells, the transformation of domain integrals to the boundary is carried out by employing the radial integration method and approximating the normalized temperature with the use of the compactly supported fourth-order spline radial basis function combined with the polynomials in global coordinates. Finally, a pure boundary element algorithm with some selected internal nodes is established for the analysis of steady convection-conduction problems with spatially variable velocity and thermal conductivity. Three numerical examples are given to demonstrate the accuracy and effectiveness of the present method.