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Really TVD advection schemes for the depth-integrated transport equation
Mercier, C.; Delhez, E.J.M. (2010). Really TVD advection schemes for the depth-integrated transport equation. Ocean Modelling 33(1-2): 10-19. dx.doi.org/10.1016/j.ocemod.2009.11.004
In: Ocean Modelling. Elsevier: Oxford. ISSN 1463-5003; e-ISSN 1463-5011, more
Peer reviewed article  
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Keyword
    Marine/Coastal
Author keywords
    Finite volume; Depth-integrated models; TVD advection schemes; Flux
Authors  Top 
  • Mercier, C., more
  • Delhez, E.J.M., more
Abstract
    This paper explores the use of TVD advection schemes to solve the depth-integrated transport equation for tracers in finite volume marine models. Numerical experiments show that the blind application of the usual TVD schemes and associated flux limiters can lead to non-TVD solutions when applied in complex geometries. Spatial and/or temporal variations of the local bathymetry can indeed break the TVD property of the usual schemes. Really TVD schemes can be recovered by taking into account the local depth and its variations in the formulation of the flux limiters. Using this approach, a generalized superbee limiter is introduced and validated.
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