The problem of water entry of a rigid body with low deadrise angle is numerically simulated by means of computational fluid dynamics. The Reynolds averaged Navier-Stokes equations are employed to simulate the water and the air. The profile of the static water surface would be deformed when the flat rigid body approaches to it. The air-cushion forms when the flat rigid body touches the water surface and it will expand and shrink alternatively. We mainly find that the average of the impact force coefficient is constant with fixed entry displacement, and the oscillating period of the impact force coefficient will decrease with the time going after the air-cushion is formed.


The problems of structure water-entry slamming exist widely at the ocean engineering (Abrate, 2011; Faltinsen, 2015). When ships navigate under the atrocious sea conditions, the hull and other parts of ship will dash frequently with the water surface because of the significant pitching and heaving. Local structure failure or the entire hull vibration, even wreckage, will occur under the remarkable impacting forces (Panciroli, et al. 2013; Faltinsen, 2015).

Significant work on this water entry problem was firstly introduced by developing an analytical formula which allows estimation of the maximum pressure on seaplane floats during water landing (von Karman, 1929). Wagner (1936) modified the von Karman's solution by taking into account the effect of water splashing on the body. The first numerical complete solution to water entry was obtained by Dobrovol'skaya (1969).

Zhao & Faltinsen (1993) introduced a complement to Wagner's studies, with linear approximation of the free-surface boundary condition for the two-dimensional impact problem. Mei et al. (1999) proposed a purely analytical method of resolution for the global two-dimensional impact problem of arbitrary bodies. Moreover Yettou et al. (2007) took into account the effect of velocity reduction of the solid body upon impact in order to determine impact pressure as well as the overall force acting on the body. While Lu et al. (2000) included the elastic deformation of the wedge in their analysis. Wu et al. (2004) carried out a numerical and experimental study of this problem. And a new iteration algorithm is proposed, in which the free surface boundary conditions were transformed to integral forms, and the developed jet was modelled through the shallow water equation. This method was extended by Xu et al. (2008) for the problem of oblique water entry of an asymmetric wedge. The problem was also solved by Semonov & Iafrati (2006) using a kind of mapping method for the complex potential.

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