A harmonic polynomial method based on Cartesian grids with local refinement for complex wave-body interactions

Abstract

A novel numerical method is proposed for complex potential free-surface flows of incompressible liquids with and without bodies. The present method combines high-order harmonic polynomials with Cartesian grids with local refinement, which can accurately represent highly-deformed free-surface boundaries and complicate body geometries and significantly reduce the errors induced by the space discretization of the governing equations of potential flows, i.e. the Laplace equation. The discretized matrix system is sparse and can be solved efficiently. Combining with proper time-stepping schemes, the present method can stably represent the potential flows in the time domain. These properties make it possible to solve fully nonlinear wave-body interactions in an accurate, stable and efficient manner, for instance, the plunging breakers, water entry of solid objects, and fully nonlinear numerical wave tank (NWT).