Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Bedload transport in shallow water models: why splitting (may) fail, how hyperbolicity (can) help

Abstract : In this paper, we are concerned with models for sedimentation transport consisting of a shallow water system coupled with a so called Exner equation that described the evolution of the topography. We show that, for some model of the bedload transport rate including the well-known Meyer-Peter and Mu ̈ller model, the system is hyperbolic and, thus, linearly stable, only under some constraint on the velocity. In practical situations, this condition is hopefully fulfilled. The numerical approximations of such system are often based on a splitting method, solving first shallow water equation on a time step and, after updating the topography. It is proved that this strategy can create spurious/unphysical oscillations which are related to the study of hyperbolicity e.g. the sign of some eigenvalue of the coupled system differs from the splitting one. Some numerical results are given to illustrate these problems and the way to overcome them in some cases using an stronger C.F.L. condition.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [24 references]  Display  Hide  Download
Contributor : Stéphane Cordier <>
Submitted on : Sunday, January 23, 2011 - 2:27:09 PM
Last modification on : Monday, December 14, 2020 - 4:50:25 PM
Long-term archiving on: : Tuesday, November 6, 2012 - 12:00:51 PM


Files produced by the author(s)


  • HAL Id : hal-00536267, version 2



Stéphane Cordier, Minh Le, Tomas Morales de Luna. Bedload transport in shallow water models: why splitting (may) fail, how hyperbolicity (can) help. 2010. ⟨hal-00536267v2⟩



Record views


Files downloads