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An unconditionally stable finite element-finite volume pressure correction scheme for the drift-flux model

Published online by Cambridge University Press:  27 January 2010

Laura Gastaldo ,
Raphaèle Herbin  and
Jean-Claude Latché
Laura Gastaldo
Affiliation:
Institut de Radioprotection et de Sûreté Nucléaire (IRSN), France. laura.gastaldo@irsn.fr; jean-claude.latche@irsn.fr
Raphaèle Herbin
Affiliation:
Université de Provence, France. herbin@cmi.univ-mrs.fr
Jean-Claude Latché
Affiliation:
Institut de Radioprotection et de Sûreté Nucléaire (IRSN), France. laura.gastaldo@irsn.fr; jean-claude.latche@irsn.fr
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Abstract

We present in this paper a pressure correction scheme for the drift-flux model combining finite element and finite volume discretizations, which is shown to enjoy essential stability features of the continuous problem: the scheme is conservative, the unknowns are kept within their physical bounds and, in the homogeneous case (i.e. when the drift velocity vanishes), the discrete entropy of the system decreases; in addition, when using for the drift velocity a closure law which takes the form of a Darcy-like relation, the drift term becomes dissipative. Finally, the present algorithm preserves a constant pressure and a constant velocity through moving interfaces between phases. To ensure the stability as well as to obtain this latter property, a key ingredient is to couple the mass balance and the transport equation for the dispersed phase in an original pressure correction step. The existence of a solution to each step of the algorithm is proven; in particular, the existence of a solution to the pressure correction step is derived as a consequence of a more general existence result for discrete problems associated to the drift-flux model. Numerical tests show a near-first-order convergence rate for the scheme, both in time and space, and confirm its stability.

Keywords

Drift-flux modelpressure correction schemesfinite volumesfinite elements
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 44 , Issue 2 , March 2010 , pp. 251 - 287
Copyright
© EDP Sciences, SMAI, 2010

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