A Hybrid Primitive-Conservative Upwind Scheme for the Drift Flux Model

Abstract

We consider a drift flux model describing one-dimensional isothermal gas-liquid flow in a long pipeline. The model consists of equations for the conservation of mass for each of the phases and the conservation of momentum of the mixture. In addition, an equation — the so-called gas slip relation — is supplied which relates the velocities of the two phases at any point. We present and demonstrate a high-resolution hybrid primitive-conservative upwind scheme, which utilise a simple non-conservative MUSCL scheme in shock free flow regions and a fully numerical, conservative Roe scheme in shocked flow regions. The overall conclusion of the numerical tests is that the hybrid upwind scheme is as accurate as the conservative Roe scheme. The hybrid scheme is, however, more efficient.