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A Preconditioned implicit Roe's scheme for barotropic flows: towards simulation of cavitation phenomena

Edoardo Sinibaldi 1 François Beux Maria Vittoria Salvetti
1 SMASH - Simulation, modeling and analysis of heterogeneous systems
CRISAM - Inria Sophia Antipolis - Méditerranée , Université de Provence - Aix-Marseille 1
Abstract : The discretisation of the Euler equations for a barotropic state law is considered. An upwind scheme based on the definition of a Roe's type matrix is first obtained for this particular hyperbolic problem. A low Mach number asymptotic study is performed both in the continuous and discrete case showing that the discrete solution admits pressure fluctuations in space much larger than those of the exact one. This is the same kind of behaviour observed for the case of a polytropic state law. A preconditioning is then applied such that the obtained discrete formulation has an asymptotic behaviour in agreement with the continuous case. A linearised implicit scheme is defined using the properties of the Roe matrix instead of the first-order homogeneity of the flux function which is not satisfied here. The implicit formulation is also extended to the preconditioned scheme. All the proposed ingredients are validated in the case of a quasi 1-D nozzle flow of a cavitating liquid.
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Submitted on : Tuesday, May 23, 2006 - 6:32:58 PM
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Edoardo Sinibaldi, François Beux, Maria Vittoria Salvetti. A Preconditioned implicit Roe's scheme for barotropic flows: towards simulation of cavitation phenomena. RR-4891, INRIA. 2003. ⟨inria-00071691⟩

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