The approximate Riemann solver of Roe applied to a drift-flux two-phase flow model

Tore Flåtten; Svend Tollak Munkejord

ESAIM: Mathematical Modelling and Numerical Analysis (2006)

  • Volume: 40, Issue: 4, page 735-764
  • ISSN: 0764-583X

Abstract

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We construct a Roe-type numerical scheme for approximating the solutions of a drift-flux two-phase flow model. The model incorporates a set of highly complex closure laws, and the fluxes are generally not algebraic functions of the conserved variables. Hence, the classical approach of constructing a Roe solver by means of parameter vectors is unfeasible. Alternative approaches for analytically constructing the Roe solver are discussed, and a formulation of the Roe solver valid for general closure laws is derived. In particular, a fully analytical Roe matrix is obtained for the special case of the Zuber–Findlay law describing bubbly flows. First and second-order accurate versions of the scheme are demonstrated by numerical examples.

How to cite

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Flåtten, Tore, and Munkejord, Svend Tollak. "The approximate Riemann solver of Roe applied to a drift-flux two-phase flow model." ESAIM: Mathematical Modelling and Numerical Analysis 40.4 (2006): 735-764. <http://eudml.org/doc/249726>.

@article{Flåtten2006,
abstract = { We construct a Roe-type numerical scheme for approximating the solutions of a drift-flux two-phase flow model. The model incorporates a set of highly complex closure laws, and the fluxes are generally not algebraic functions of the conserved variables. Hence, the classical approach of constructing a Roe solver by means of parameter vectors is unfeasible. Alternative approaches for analytically constructing the Roe solver are discussed, and a formulation of the Roe solver valid for general closure laws is derived. In particular, a fully analytical Roe matrix is obtained for the special case of the Zuber–Findlay law describing bubbly flows. First and second-order accurate versions of the scheme are demonstrated by numerical examples. },
author = {Flåtten, Tore, Munkejord, Svend Tollak},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Two-phase flow; drift-flux model; Riemann solver; Roe scheme.; Zuber-Findlay law; bubbly flows},
language = {eng},
month = {11},
number = {4},
pages = {735-764},
publisher = {EDP Sciences},
title = {The approximate Riemann solver of Roe applied to a drift-flux two-phase flow model},
url = {http://eudml.org/doc/249726},
volume = {40},
year = {2006},
}

TY - JOUR
AU - Flåtten, Tore
AU - Munkejord, Svend Tollak
TI - The approximate Riemann solver of Roe applied to a drift-flux two-phase flow model
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2006/11//
PB - EDP Sciences
VL - 40
IS - 4
SP - 735
EP - 764
AB - We construct a Roe-type numerical scheme for approximating the solutions of a drift-flux two-phase flow model. The model incorporates a set of highly complex closure laws, and the fluxes are generally not algebraic functions of the conserved variables. Hence, the classical approach of constructing a Roe solver by means of parameter vectors is unfeasible. Alternative approaches for analytically constructing the Roe solver are discussed, and a formulation of the Roe solver valid for general closure laws is derived. In particular, a fully analytical Roe matrix is obtained for the special case of the Zuber–Findlay law describing bubbly flows. First and second-order accurate versions of the scheme are demonstrated by numerical examples.
LA - eng
KW - Two-phase flow; drift-flux model; Riemann solver; Roe scheme.; Zuber-Findlay law; bubbly flows
UR - http://eudml.org/doc/249726
ER -

References

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