# Simulation numérique en volume finis, de problèmes d'écoulements multidimensionnels raides, par un schéma de flux à deux pas

Abstract : This thesis is devoted to the numerical simulation of stiff fluid flows, governed by systems of conservation laws with source terms (non homogeneous systems). Both one dimensional and two-dimensional configurations are considered. The numerical method used is an extension of the two steps flux scheme (SRNH), which depends on a local adjustable parameter \alpha^n_(j+\frac(1)(2)), and which has been proposed by professor F.Benkhaldoun in the one dimensional framework. In a first part of the work, aiming to extend the scheme to the two-dimensional case, we introduce an alternative scheme (SRNHR), which is obtained from $SRNH$ by replacing the numerical velocity (\frac(\Delta x)(\Delta t)), by the local physical Rusanov velocity. Thereafter, the stability analysis of the scheme, shows that the new scheme can be of order 1 or 2 according to the value of the parameter \alpha^n_(j+\frac(1)(2)). A strategy of variation of this parameter, based on limiters theory was then adopted. The scheme can thus be turned to order 1 in the regions where the flow has a strong variation, and to order 2 in the regions where the flow is regular. After this step, we established the conditions so that this scheme respects the exact C-property introduced by Bermùdez and Vazquez. A study of boundary conditions, adapted to this kind of two steps schemes, has also been carried out using the Riemann invariants. In the second part of the thesis, we applied this new scheme to homogeneous and nonhomogeneous monophasic systems. For example, we performed the numerical simulation of shallow water phenomena with bottom topography in both one and two dimensions. We also carried out a numerical convergence study by plotting the error curves. Finally, we used the scheme for the numerical simulation of two phase flow models ( Ransom 1D and 2D).
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Theses
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https://tel.archives-ouvertes.fr/tel-00010794
Contributor : Kamel Mohamed <>
Submitted on : Friday, October 28, 2005 - 11:43:40 AM
Last modification on : Tuesday, October 20, 2020 - 3:56:19 PM
Long-term archiving on: : Monday, September 20, 2010 - 1:06:16 PM

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• HAL Id : tel-00010794, version 2

### Citation

Kamel Mohamed. Simulation numérique en volume finis, de problèmes d'écoulements multidimensionnels raides, par un schéma de flux à deux pas. Mathématiques [math]. Université Paris-Nord - Paris XIII, 2005. Français. ⟨tel-00010794v2⟩

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