A staggered scheme for hyperbolic conservation laws applied to unsteady sheet cavitation

Abstract.We demonstrate the advantages of discretizing on a staggered grid for the computation of solutions to hyperbolic systems of conservation laws arising from instationary flow of an inviscid fluid with an arbitrary equation of state. Results for a highly nonlinear, nonconvex equation of state obtained with the staggered discretisation are compared with those obtained with the Osher scheme for two different Riemann problems. The staggered approach is shown to be superior in simplicity and efficiency, without loss of accuracy. The method has been applied to simulate unsteady sheet cavitation on a NACA0012 hydrofoil. Results show good agreement with those obtained with a cavity interface tracking method.