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A modified TVD scheme for the advection of two or more variables with consideration for their sum
Mercier, C.Y.M.; Delhez, E.J.M. (2010). A modified TVD scheme for the advection of two or more variables with consideration for their sum. Ocean Dynamics 60(5): 1157-1166. dx.doi.org/10.1007/s10236-010-0315-1
In: Ocean Dynamics. Springer-Verlag: Berlin; Heidelberg; New York. ISSN 1616-7341, more
Peer reviewed article  

Available in Authors 
    VLIZ: Open Repository 279079 [ OMA ]

Keyword
    Marine
Author keywords
    TVD schemes; Sum of variables; Slope limiters; Superbee; Minmod; Totalvariation; Advection; Tracer

Authors  Top 
  • Mercier, C.Y.M., more
  • Delhez, E.J.M., more

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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