Reference : Consistent computation of the age of water parcels using CART
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Earth sciences & physical geography
Consistent computation of the age of water parcels using CART
Mercier, Christophe mailto [Université de Liège - ULg > Département d'aérospatiale et mécanique > Mathématiques générales >]
Delhez, Eric mailto [Université de Liège - ULg > Département d'aérospatiale et mécanique > Mathématiques générales >]
Ocean Modelling
Elsevier Science
Yes (verified by ORBi)
United Kingdom
[en] TVD schemes ; Maximum principle ; Superbee ; Age ; Slope limiter ; model diagnostic ; CART ; ocean modeling
[en] The Constituent-oriented Age and Residence time Theory (CART) provides a flexible and efficient framework to diagnose the dynamics of marine systems. Beside the equation for the concentration of appropriate (real or artificial) tracers, the method requires the resolution of differential problems for the so-called age concentration of each of these tracers. Thanks to its Eulerian formulation as an advection/diffusion problem with source terms, the method is easily implemented in existing models. However, some numerical artifacts should be avoided in order to produce physically meaningful results leading to a better understanding of the system under study. In this paper, we address two such issues that are related to the degree of implicitness of the different terms and to the advection scheme.

To enforce the consistency between the discrete equations for the concentration of a tracer and for its age concentration, the degree of implicitness must be identical in the source/sink terms of the two equations. However, the ageing term should be computed in a completely explicit (respectively implicit) way if the discretization of the source/sink terms is implicit in time (respectively explicit).

A specific attention should also be paid to the advection schemes for the concentration and the age concentration. The raw application of Total Variation Diminishing (TVD) scheme for both equations can lead to the occurrence of artificial local extreme values and spatial oscillations of the age field. While the TVD behavior of the discrete age field cannot be guaranteed, appropriate modifications of the flux/slope limiters used in the TVD schemes can be implemented to enforce a maximum principle that prevents the occurrence of age values outside the physically acceptable range.
Centre Interfacultaire de Recherches en Océanologie - MARE

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