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.
@article{M2AN_2006__40_4_735_0,
author = {Fl\aa tten, Tore and Munkejord, Svend Tollak},
title = {The approximate Riemann solver of Roe applied to a drift-flux two-phase flow model},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {40},
year = {2006},
pages = {735-764},
doi = {10.1051/m2an:2006032},
mrnumber = {2274776},
zbl = {1123.76038},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2006__40_4_735_0}
}
Flåtten, Tore; Munkejord, Svend Tollak. The approximate Riemann solver of Roe applied to a drift-flux two-phase flow model. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 40 (2006) pp. 735-764. doi : 10.1051/m2an:2006032. http://gdmltest.u-ga.fr/item/M2AN_2006__40_4_735_0/
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