PAVAN, Sara; HERVOUËT, Jean-Michel; RICCHIUTO, Mario; ATA, Riadh

doi:10.1016/j.jcp.2016.04.053

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PAVAN, Sara
Simulation et Traitement de l'information pour l'Exploitation des systèmes de Production [EDF R&D STEP]
Laboratoire d'Hydraulique Saint-Venant / Saint-Venant laboratory for Hydraulics [LHSV]

HERVOUËT, Jean-Michel
Simulation et Traitement de l'information pour l'Exploitation des systèmes de Production [EDF R&D STEP]

RICCHIUTO, Mario
Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts [CARDAMOM]

Langue

Article de revue

Ce document a été publié dans

Journal of Computational Physics. 2016, vol. 318, p. 122 - 141

Elsevier

Résumé en anglais

We present a second order residual distribution scheme for scalar transport problems in shallow water flows. The scheme, suitable for the unsteady cases, is obtained adapting to the shallow water context the explicit Runge-Kutta schemes for scalar equations [1]. The resulting scheme is decoupled from the hydrodynamics yet the continuity equation has to be considered in order to respect some important numerical properties at discrete level. Beyond the classical characteristics of the residual formulation presented in [1] and [2], we introduce the possibility to iterate the corrector step in order to improve the accuracy of the scheme. Another novelty is that the scheme is based on a precise monotonicity condition which guarantees the respect of the maximum principle. We thus end up with a scheme which is mass conservative, second order accurate and monotone. These properties are checked in the numerical tests, where the proposed approach is also compared to some finite volume schemes on unstructured grids. The results obtained show the interest in adopting the predictor corrector scheme for pollutant transport applications, where conservation of the mass, monotonicity and accuracy are the most relevant concerns.< Réduire

DOI

http://dx.doi.org/10.1016/j.jcp.2016.04.053

Project ANR

Tsunamis en Atlantique et MaNche : Définition des Effets par Modélisation - ANR-11-RSNR-0023

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251