Higher-order boundary element methods for unsteady convective transport

Higher-order boundary element methods (BEM) are presented for time-dependent convective diffusion problems. The time-dependent convective diffusion free-space fundamental solutions originally proposed by Carslaw and Jaeger are used to obtain the boundary integral formulation. For the linear, quadratic and quartic time interpolation functions considered in this paper, a complete set of closed form time integrals for the one-dimensional formulation are developed. Boundary element method solutions are obtained for four problems of unsteady convection-diffusion, including shock wave propagation. It is shown that the BEM solutions are extremely accurate hi contrast to finite-difference and finite-element methods. Moreover, no upwinding is needed for the boundary element methods, even for high Peclet number flows. Finally, the conventional BEM formulation is extended to a problem involving singular flux arising due to a sudden rise of temperature on the boundary. This infinite flux BEM formulation provides significantly more accurate numerical results than the conventional approach.