An unconditionally stable finite element-finite volume pressure correction scheme for the drift-flux model
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 44 (2010) no. 2, p. 251-287

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.

DOI : https://doi.org/10.1051/m2an/2010002
Classification:  65N12,  65N30,  76N10,  76T05,  76M25
Keywords: drift-flux model, pressure correction schemes, finite volumes, finite elements
@article{M2AN_2010__44_2_251_0,
author = {Gastaldo, Laura and Herbin, Rapha\`ele and Latch\'e, Jean-Claude},
title = {An unconditionally stable finite element-finite volume pressure correction scheme for the drift-flux model},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {44},
number = {2},
year = {2010},
pages = {251-287},
doi = {10.1051/m2an/2010002},
zbl = {pre05692906},
mrnumber = {2655950},
language = {en},
url = {http://www.numdam.org/item/M2AN_2010__44_2_251_0}
}
Gastaldo, Laura; Herbin, Raphaèle; Latché, Jean-Claude. An unconditionally stable finite element-finite volume pressure correction scheme for the drift-flux model. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 44 (2010) no. 2, pp. 251-287. doi : 10.1051/m2an/2010002. http://www.numdam.org/item/M2AN_2010__44_2_251_0/

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