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Overland flow modelling with the Shallow Water Equation using a well balanced numerical scheme: Adding efficiency or just more complexity?

Marie Rousseau 1, 2, Olivier Cerdan 1, Olivier Delestre 3, 4, Fabrice Dupros 1, Francois James 3, Stéphane Cordier 3

(2012-01-30)

In the last decades, more or less complex physically-based hydrological models, have been developed that solve the shallow water equations or their approximations using various numerical methods. Model users may not necessarily know the different hypothesis lying behind these development and simplifications, and it might therefore be difficult to judge if a code is well adapted to their objectives and test case configurations. This paper aims at comparing the predictive abilities of different models and evaluating potential gain by using advanced numerical scheme for modelling runoff. We present four different codes, each one based on either shallow water or kinematic waves equations, and using either finite volume or finite difference method. We compare these four numerical codes on different test cases allowing to emphasize their main strengths and weaknesses. Results show that, for relatively simple configurations, kinematic waves equations solved with finite volume method represent an interesting option. Nevertheless, as it appears to be limited in case of discontinuous topography or strong spatial heterogeneities, for these cases we advise the use of shallow water equations solved with the finite volume method.

1:	Bureau de recherches géologiques et minières (BRGM)
	Bureau de Recherches Géologiques et Minières (BRGM)
2:	Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS)
	Ecole des Ponts ParisTech
3:	Mathématiques - Analyse, Probabilités, Modélisation - Orléans (MAPMO)
	Université d'Orléans – CNRS : UMR7349
4:	Laboratoire Jean Alexandre Dieudonné (JAD)
	CNRS : UMR6621 – Université Nice Sophia Antipolis [UNS]

Research team: RIS/RMT

Subject

:

Computer Science/Modeling and Simulation

Keyword(s): overland flow – well-balanced finite volume scheme – finite differences scheme – kinematic wave equations – shallow water equations – comparison of numerical models

hal-00664535, version 1

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From: Marie Rousseau <>

Submitted on: Monday, 30 January 2012 18:53:01

Updated on: Tuesday, 31 January 2012 09:32:18