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 high-resolution hybrid primitive-conservative upwind schemes, which utilise a simple non-conservative MUSCL scheme in shock free flow regions and high-resolution conservative upwind schemes in shocked flow regions. We apply these hybrid schemes to various test problems and compare them with some conservative upwind schemes. The overall conclusion is that the hybrid upwind schemes are as accurate as the corresponding conservative schemes. The hybrid schemes are, however, more efficient.
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