A new numerical strategy for the resolution of high-Péclet advection–diffusion problems

This paper introduces a discontinuous method for the efficient determination of an approximate numerical solution of the two-dimensional advection–diffusion equation. Using the VTCR methodology (see [1]), this method involves free-space solutions of the governing partial differential equation. For the advection–diffusion equation with constant coefficients, the free-space solutions are exponential functions with a sharp gradient. The continuity of the solution across element boundaries is enforced weakly through a dedicated variational formulation. Preliminary results for a certain type of benchmark problem suggest that this approach is a promising numerical tool for handling such problems.