Liquid and liquid-gas flows at all speeds : Reference solutions and numerical schemes

This paper present some reference solutions to be used in order to validate and improve numerical schemes for multiphase flows. We address here exact one-dimensional liquid and liquid-gas compressible flows solutions in nozzles. The exact solution is first derived for the compressible single liquid phase Euler equations and extends the well known ideal gas dynamic nozzle flow solutions.The all Mach number scheme is then derived. A preconditioned Riemann solver is built and embedded into the Godunov explicit scheme. It is shown that this method converges to exact solutions but needs too small time steps to be efficient. An implicit version is then derived, in one dimension first and second in the frame of 3D unstructured meshes