A positive spatial advection scheme on triangular meshes for tracer transport

Authors:
P. Wilders
Affiliations:
Dept. of Information Technology and Systems, Delft University, P.O. Box 5031, 2600 GA Delft, The Netherlands
Venue:
Scientific computing and applications
Year:
2001

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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 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.