In spite of the absence of shock waves in most hydrodynamic applications, sufficient reason remains to employ Godunov-type schemes in this field. In the instance of two-phase flow, the shock capturing ability of these schemes may serve to maintain robustness and accuracy at the interface. Moreover, approximate Riemann solvers have greatly relieved the initial drawback of computational expensiveness of Godunov-type schemes. In the present work we develop an Osher-type flux-difference splitting approximate Riemann solver and we examine its application in hydrodynamics. Actual computations are left to future research.

Conservation laws (msc 35L65), Shocks and singularities (msc 35L67), Shock waves and blast waves (msc 76L05), None of the above, but in MSC2010 section 74Hxx (msc 74H99), Surface waves (msc 74J15), Two-phase and multiphase flows (msc 76Txx)
Modelling, Analysis and Simulation [MAS]

van Brummelen, E.H. (1998). A Godunov-type scheme with applications in hydrodynamics. Modelling, Analysis and Simulation [MAS]. CWI.