A new averaging scheme for the riemann problem in pure water

The numerical investigation of shock phenomena in gas or liquid media where enthalpy is the preferred thermodynamic variable poses special problems. When an expression for internal energy is available, the usual procedure is to employ a splitting scheme to remove source terms from the Euler equations, then upwind-biased shock capturing algorithms are built around the Riemann problem for the conservative system which remains. However, when the governing equations arc formulated in terms of total enthalpy, treatment of a pressure time derivative as a source term leads to a Riemann problem for a system where one equation is not a conservation law. The present research establishes that successful upwind-biased shock capturing schemes can be based upon the pseudo-conservative system. A new averaging scheme for solving the associated Riemann problem is developed. The method is applied to numerical simulations of shock wave propagation in pure water.