A positive spatial advection scheme on unstructured meshes for tracer transport

摘要

Modelling tracer transport (leading to a single linear advection–diffusion equation) for realistic data provides a challenging task with respect to the robustness of the underlying numerical procedures. In this paper, we contribute at this point by formulating a positive spatial advection scheme for unstructured triangular meshes. The proof of positivity is presented in detail, using an elementary classification. It is shown that with a careful reconstruction procedure and a moderate demand towards the grid a positive advection scheme is obtained. Next, a brief discussion is given on how we implement this scheme in combination with an implicit time-stepping procedure. As a numerical example, we discuss tracer transport in a strongly heterogeneous porous medium.