A positive spatial advection scheme on unstructured meshes for tracer transport

Authors:
P. Wilders;G. Fotia
Affiliations:
Department of Information Technology and Systems, Delft University, P.O. Box 5031, 2600 GA Delft, Netherlands;Scientific Research Division, CRS4, VI Strada OVEST Z.I. Macchiareddu, 09010 UTA Cagliari, Italy
Venue:
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
Year:
2002

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Abstract

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.