We construct a Roe-type numerical scheme for approximating the solutionsof a drift-flux two-phase flow model. The model incorporates a set ofhighly 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 bynumerical examples.
