Numerical simulation of depth-averaged flow models : a class of Finite Volume and discontinuous Galerkin approaches.

Abstract : This work is devoted to the development of numerical schemes to approximate solutions of depth averaged flow models. We first detail the construction of Finite Volume approaches for the Shallow Water system with source terms on unstructured meshes. Based on a suitable reformulation of the equations, we implement a well-balanced and positivepreserving approach, and suggest adapted MUSCL extensions. The method is shown to handle irregular topography variations and demonstrates strong stabilities properties. The inclusion of friction terms is subject to a thorough analysis, leading to the establishment of some Asymptotic Preserving property through the enhancement of another recent Finite Volume scheme. The second aspect of this study concerns discontinuous Galerkin Finite- Element methods. Some of the ideas advanced in the Finite Volume context are employed to broach the Shallow Water system on triangular meshes. Numerical results are exposed and the method turns out to be well suited to describe a large variety of flows. On these observations we finally propose to exploit its features to extend the approach to a new family of Green-Nadghi equations. Numerical experiments are also proposed to validate this numerical model.
Complete list of metadatas

https://tel.archives-ouvertes.fr/tel-01109438
Contributor : Arnaud Duran <>
Submitted on : Monday, January 26, 2015 - 12:51:09 PM
Last modification on : Saturday, January 27, 2018 - 1:31:32 AM
Long-term archiving on : Monday, April 27, 2015 - 10:25:17 AM

Identifiers

  • HAL Id : tel-01109438, version 1

Collections

Citation

Arnaud Duran. Numerical simulation of depth-averaged flow models : a class of Finite Volume and discontinuous Galerkin approaches.. Numerical Analysis [math.NA]. Université Montpellier II, 2014. English. ⟨tel-01109438⟩

Share

Metrics

Record views

522

Files downloads

774