# Congrès d'Analyse Numérique pour les Jeunes - 2020

Dec 3 – 4, 2020
Virtuel
Europe/Paris timezone

## A general comparison between the solutions generated by the FVC scheme and di erent exact solutions

Dec 3, 2020, 12:00 PM
30m
Zoom (Virtual)

### Speakers

Prof. Imad KIssami (MSDA Laboratory, University Mohammed VI Polytechnic, Benguerir, Morocco.)Prof. Fayssal Benkhaldoun (LAGA, Universite Sorbonne Paris Nord, CNRS, UMR 7539, F-93430, Villetaneuse, France.)

### Description

Hydrodynamic transport problems often take the form of hyperbolic conservation law systems (see e.g. [6, 5]). In this work we will focus on the Saint-Venant system which is still the utmost important model in maritime or fuvial hydraulics simulations, it governs the free surface shallow water flows. It was obtained from Navier-Stokes equations using adequate assumptions see [7]. Due to their widely recognized experimental validity and numerical effciency, the Saint-Venant equations are now widely used for many current simulations: environmental protection, environmental pollution, natural disasters, climate change, dam failure, tidal calculations, flood studies, sedimentology, etc. We are mainly interested in the numerical resolution of this system using a robust scheme called FVC. This scheme is accurate, conservative and solve the non-linear conservation laws without Riemann Solvers, it has been presented in several works e.g. [8, 3, 2].
In this paper, we will compare our FVC approach, using unstructured 2-D meshes, to some exact solutions for shallow water system, present in the literature, under the infuence of the gravity, the Coriolis force, and other frictional forces effects see [4, 1].

Key-words: Shallow water system, Free surface fows, Finite volume method, Exact solutions , FVC.

References:
[1] F. Alcrudo and F. Benkhaldoun. Exact solutions to the riemann problem of the shallow water equations Computers & Fluids, 30(6):643{671, 2001.
[2] F. Benkhaldoun, S. Sari, and M. Seaid. Projection ?nite volume method for shallow water fows. Mathematics and computers insimulation, 118:87{101, 2015.
[3] F. Benkhaldoun and M. Seaid. A simple ?nite volume method for the shallow water equations. Journal of computational and applied mathematics, 234(1):58{72, 2010.
[4] O. Delestre, C. Lucas, P.-A. Ksinant, F. Darboux, C. Laguerre, T.-N.-T. Vo, F. James, and S. Cordier. Swashes: a compilation of shallow water analytic solutions. International Journal for Numerical Methods in Fluids, 72(3):269{300, 2013.
[5] E. Godlewski and P.-A. Raviart. Numerical approximation of hyperbolic systems of conservation laws, volume 118. Springer, 1996.
[6] R. J. LeVeque and R. J. Leveque. Numerical methods for conservation laws, volume 132. Springer, 1992.
[7] A. d. Saint-Venant, D. Barr?e, J. Saint-Cyr, V. de Saint, AA. SAINT-VENANT, D. BARR?E, and J. Saint-du mouvement non-permanent des eaux, avec application aux crues des rivi?eres et ?e l'introduction. 1871.
[8] M. Ziggaf, M. Boubekeur, F. Benkhaldoun, I. El Mahi, et al. The fvc scheme on unstructured meshes for the two-dimensional
shallow water equations. In International Conference on FV for Complex Applications, pages 455{465. Springer, 2020.

### Primary authors

Moussa Ziggaf (LAGA, Universite Sorbonne Paris Nord, CNRS, UMR 7539, F-93430, Villetaneuse, France/ENSAO, LM2N, Complexe Universitaire, B.P. 669, 60000 Oujda, Morocco.) Prof. Imad KIssami (MSDA Laboratory, University Mohammed VI Polytechnic, Benguerir, Morocco.)

### Co-authors

Dr Mohamed Boubekeur (LAGA, Universite Sorbonne Paris Nord, CNRS, UMR 7539, F-93430, Villetaneuse, France.) Prof. Fayssal Benkhaldoun (LAGA, Universite Sorbonne Paris Nord, CNRS, UMR 7539, F-93430, Villetaneuse, France.)