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

Abstract

Abstract.We construct a Roe-type numerical scheme for approximating the solutions of a driftflux 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.Mathematics Subject Classification. 35L65, 76M12, 76T10.

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