A modified TVD scheme for the advection of two or more variables with consideration for their sum |
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Authors: | Christophe Y M Mercier Eric J M Delhez |
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Institution: | 1. Modélisation et Méthodes Mathématiques, Département Aérospatiale et Mécanique, Université de Liège, Sart-Tilman B37, B-4000, Liège, Belgium
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Abstract: | Total variation diminishing (TVD) advection schemes are known to produce results that are free from some of the numerical
artifacts (no overshooting, no spurious oscillation, small diffusion) that can spoil the physical significance of the results.
When two or more tracers are advected separately using a TVD scheme, the sum of these variables can however exhibit some inappropriate
behaviors. The total variation of the sum will not necessarily be non- increasing and local artificial oscillations and extrema
can appear. We show that these can be avoided with only minor perturbations of the original solution by adjusting the slope
limiters used for the different variables. If the sum of these variables has some physical significance, for instance as refinement
of a larger model compartment, the correction procedure introduced in this paper should be used to ensure a physically meaningful
solution. |
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