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

Laura Gastaldo; Raphaèle Herbin; Jean-Claude Latché

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 44, Issue: 2, page 251-287
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Gastaldo, Laura, Herbin, Raphaèle, and Latché, Jean-Claude. "An unconditionally stable finite element-finite volume pressure correction scheme for the drift-flux model." ESAIM: Mathematical Modelling and Numerical Analysis 44.2 (2010): 251-287. <http://eudml.org/doc/250805>.

@article{Gastaldo2010,
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. },
author = {Gastaldo, Laura, Herbin, Raphaèle, Latché, Jean-Claude},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Drift-flux model; pressure correction schemes; finite volumes; finite elements; drift-flux model},
language = {eng},
month = {3},
number = {2},
pages = {251-287},
publisher = {EDP Sciences},
title = {An unconditionally stable finite element-finite volume pressure correction scheme for the drift-flux model},
url = {http://eudml.org/doc/250805},
volume = {44},
year = {2010},
}

TY - JOUR
AU - Gastaldo, Laura
AU - Herbin, Raphaèle
AU - Latché, Jean-Claude
TI - An unconditionally stable finite element-finite volume pressure correction scheme for the drift-flux model
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 44
IS - 2
SP - 251
EP - 287
AB - 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.
LA - eng
KW - Drift-flux model; pressure correction schemes; finite volumes; finite elements; drift-flux model
UR - http://eudml.org/doc/250805
ER -

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