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, Volume 40 (2006) no. 4, p. 735-764

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.

DOI : https://doi.org/10.1051/m2an:2006032
Classification:  35L65,  76M12,  76T10
Keywords: two-phase flow, drift-flux model, Riemann solver, Roe scheme
@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},
     publisher = {EDP-Sciences},
     volume = {40},
     number = {4},
     year = {2006},
     pages = {735-764},
     doi = {10.1051/m2an:2006032},
     zbl = {1123.76038},
     mrnumber = {2274776},
     language = {en},
     url = {http://www.numdam.org/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, Volume 40 (2006) no. 4, pp. 735-764. doi : 10.1051/m2an:2006032. http://www.numdam.org/item/M2AN_2006__40_4_735_0/

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