Numerical solution of convection-diffusion problems at high Péclet number using boundary elements

This paper describes a boundary element scheme for solving steady-state convection–diffusion problems at high Péclet numbers. A special treatment of the singular integrals is included which uses discontinuous elements and a regularization procedure. Transformations are performed to avoid directly evaluating Bessel functions for Cauchy principal value and hypersingular integrals. Test examples are solved with values of Péclet number up to 107 to assess the numerical scheme.