AN IMPROVED MAC METHOD (SIMAC) FOR UNSTEADY HIGH-REYNOLDS FREE SURFACE FLOWS

Abstract

A modified MAC method (SIMAC; semi-implicit marker and cell) is proposed which accurately treats unsteady high-Reynolds free surface problems. SIMAC solves the Navier–Stokes equations in primitive variables on a non-uniform staggered Cartesian grid by means of a finite difference scheme. The convective term is treated explicitly by employing a second-order upwind scheme in space (HLPA) and the Adams–Bashforth technique in time. The diffusive part is solved by means of the implicit approximate factorization technique. A multigrid technique based on the additive correction strategy is employed to solve the Poisson equation for the pressure. Finally, the free surface treatment is carried out using massless particles which divide the domain of integration into full and empty cells as in a standard MAC method. The algorithm is used for the analysis of large-amplitude water sloshing in rectangular unbaffled and baffled containers. Experimental tests have been carried out in order to validate the algorithm. Numerical results satisfactorily agree with experimental data for the whole range of filing conditions analysed here. © 1997 by John Wiley & Sons, Ltd.