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

¹ The International Research Institute of Stavanger, Prof. Olav Hanssensvei 15, Stavanger, Norway. Tore.Flaatten@irisresearch.no
² Current address: Centre of Mathematics for Applications, 1053 Blindern, 0316 Oslo, Norway.
³ Department of Energy and Process Engineering, Norwegian University of Science and Technology, Kolbjørn Hejes veg 1A, 7491 Trondheim, Norway. stm@pvv.ntnu.no

Received: 14 January 2006
Revised: 12 May 2006

Abstract

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.