Riemann solvers for water hammer simulations by Godunov method

The water hammer phenomenon can be described by a 2 x 2 system of hyperbolic partial differential equations (PDEs). Numerical solution of these PDEs using finite-volume schemes is investigated herein. The underlying concept of the Godunov scheme is the Riemann problem, that must be solved to provide fluxes between the computational cells. The presence of the kinetic terms in the momentum equation determines the existence of shock and rarefaction waves, which influence the design of the Riemann solver. Approximation of the expressions for the Riemann invariants and jump relationships can be used to derive first- and second-order approximate, non-iterative solvers. The first-order approximate solver is almost 2000 times faster than the exact one, but gives inaccurate predictions when the densities and celerities are low. The second-order approximate solver gives very accurate solutions, and is 300 times faster than the exact, iterative one. Detailed indications are provided in the appendices for the practical implementation of the Riemann solvers described herein. Copyright (C) 2000 John Wiley & Sons, Ltd.