no. 4
The approximate Riemann solver of Roe applied to a drift-flux two-phase flow model
ESAIM: Modélisation mathématique et analyse numérique, Tome 40 (2006) no. 4, pp. 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 : 10.1051/m2an:2006032
Classification : 35L65, 76M12, 76T10
Mots clés : two-phase flow, drift-flux model, Riemann solver, Roe scheme 
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Flåtten, Tore; Munkejord, Svend Tollak. The approximate Riemann solver of Roe applied to a drift-flux two-phase flow model. ESAIM: Modélisation mathématique et analyse numérique, Tome 40 (2006) no. 4, pp. 735-764. doi : 10.1051/m2an:2006032. http://www.numdam.org/articles/10.1051/m2an:2006032/

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