Skip Navigation



IMA Journal of Numerical Analysis Advance Access published online on September 7, 2009
IMA Journal of Numerical Analysis, doi:10.1093/imanum/drp006
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Gastaldo, L.
Right arrow Articles by Latché, J.-C.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

A discretization of the phase mass balance in fractional step algorithms for the drift-flux model

Laura Gastaldo{dagger}

Institut de Radioprotection et de Sûreté Nucléaire, BP3, 13115 St Paul-lez-Durance cedex, France

Raphaèle Herbin{ddagger}

Université de Provence, Centre de Mathématiques et Informatique, 39 rue Frédéric Joliot-Curie, 13453 Marseille cedex 13, France

Jean-Claude Latché§

Institut de Radioprotection et de Sûreté Nucléaire, BP3, 13115, St Paul-lez-Durance cedex, France

{dagger} Email: laura.gastaldo{at}irsn.fr

{ddagger} Corresponding author. Email: herbin{at}cmi.univ-mrs.fr

§ Email: jean-claude.latche{at}irsn.fr

Received on 16 October 2007. Revised on 1 August 2008.


  Abstract

We address in this paper a parabolic equation used to model the phase mass balance in two-phase flows, which differs from the mass balance for chemical species in compressible multicomponent flows by the addition of a nonlinear term of the form {nabla}·{rho}{phi}(y)ur, where y is the unknown mass fraction, {rho} stands for the density, {phi} is a regular function such that {phi}(0) = {phi}(1) = 0 and ur is a (not necessarily divergence free) velocity field. We propose a finite-volume scheme for the numerical approximation of this equation, with a discretization of the nonlinear term based on monotone flux functions. Under the classical assumption that the discretization of the convection operator must be such that it vanishes for a constant y, we prove the existence and uniqueness of the solution, together with the fact that it remains within its physical bounds, i.e., within the interval [0, 1]. Then this scheme is combined with a pressure correction method to obtain a semi-implicit fractional step scheme for the so-called drift-flux model. To satisfy the above-mentioned assumption a specific time stepping algorithm with particular approximations for the density terms is developed. Numerical tests are performed to assess the convergence and stability properties of this scheme.

Key Words: two-phase flows; drift-flux model; finite-volume methods; monotone schemes


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.