Multigrid Computations and Conservation Law Treatment of a Sharp Interface Method

ABSTRACT The sharp interface method (SIM) utilizing the Cartesian grid and cut-cell approach can solve fluid flow problems involving multiphase and/or complex geometry with second-order accuracy. Due to the algorithm and data management requirements, the SIM is computationally intensive. In this study, two issues are investigated to help further advance the SIM. First, the conservation-law property at the interface is examined in detail; an artificially assigned interface inside a single-phase, homogeneous fluid domain is devised to examine SIM's performance. Second, an interface-averaging multigrid method, accounting for the presence of irregularly shaped moving boundaries, is developed to speed up the pressure solver. The present work has demonstrated that the SIM satisfies the conservation laws numerically and has identified ways to reduce the computing time.

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