A Godunov-type scheme with applications in hydrodynamics

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.