In this paper, one phase level set method proposed by Carrica, Wilson and Stern (2005) coupled with FEM is adopted to numerically simulate the viscous flows over surface-piercing body. The advantage of the one phase level set method against the standard level set method is that the computation is implemented only in a fluid with denser constant properties and jump conditions are imposed explicitly such that no transition zone is needed, computing time for solving equations in air is saved. The flows are solved by multigrid FEM method based on FEATFLOW solver (Turek, 1999), and a fourth-order Taylor Galerkin scheme is applied to discretize the pure convection equation for level set function. Two numerical examples are presented to demonstrate the capability and efficiency of the presented method to solve complex flows of surface-piercing body in viscous fluids.


Flows over surface-piercing body are often met in the fields of coastal and offshore engineering as well as naval architecture. For example, a wave overtopping obstruction is of considerable importance in a number of hydraulic and coastal engineering applications. During the wave overtopping obstacle, many complex phenomena including water accumulation, wave run-up, water jet flows, water jet impact upon free surface, wave overturning, merging and breaking as well as nonlinear interactions between free surface flows and separating flows, will happen. Another example is the so called "green water" phenomena: when a ship travels in severe sea conditions or a turret-moored system operates in rough weather, its bow may become immersed in the water. As a result, a solid and compact mass of water will wash along and across the deck. During the process, large impact pressures and forces can occur when this block of water which may travel at high speed strikes the obstructions in its way.

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