A Mach-Uniform Strictly Conservative High-Resolution Scheme for Unsteady Compressible Flows of Gases and Liquids

Abstract

We present a new numerical method to simulate unsteady compressible flows under arbitrary Mach number condition. A hybrid explicit / fractional-step temporal discretization for Euler equation on strictly conservative formulation has been developed. The explicit method is adopted when the flow speed is high so that strong shocks as well as sound waves are accurately captured; while the fractional-step pressure-iteration method is adopted when the flow speed is low so that the CFL condition as a constraint on the time step can be avoided. We selected as the base scheme Jiang et al.'s nonstaggered version of the high-resolution central scheme by Nessyahu and Tadmor for hyperbolic conservation law since the scheme is well-suited to construct the fractional-step algorithm. An additional pressure correction procedure (GCUP) is implemented to deal with general equation of state. Riemann problems in one dimension are solved for a gas and a liquid to show high accuracy and robustness of the present scheme. A flow transition calculation from subsonic to supersonic due to a heat source is also successful.