A numerical simulation method for free surface flows near a two-dimensional moving body in fixed rectangular grid system

A numerical simulation method is developed for the description of a two-dimensional body moving in free surface flows using a fixed rectangular grid system. The nonlinear free surface is determined by the modified Marker-density method. The body boundary is defined by the line segments connecting the points where the body surface and grid lines meet. The Navier–Stokes equations and the continuity equation are used as the governing equations, which are coupled with a two-step projection method described in detail in this research. The velocities and pressures in the body boundary cells as well as the free surface cells are calculated using a simultaneous iterative method. For the verification of the present numerical method, four kinds of simulations have been conducted. The first case is to investigate the vortex shedding of an advancing cylinder, the second case is about the forced oscillation of a box, the third case is to clarify the sloshing phenomenon in a horizontally excited tank, and the last case is waves generation by a plunging-type wave maker. The simulation results are confirmed with corresponding experimental results or analytical solutions.

► A numerical method is presented for a 2-D moving body using fixed Cartesian grid.
► Modified Marker-density method is applied for nonlinear waves.
► Four kinds of simulations are carried out for the verification of the present method.