ORIGINAL ARTICLE Two-dimensional numerical simulation and experiment on strongly nonlinear wave–body interactions Changhong Hu Æ Masashi Kashiwagi Received: 30 October 2007 / Accepted: 10 July 2008 / Published online: 29 August 2008 Ó JASNAOE 2008 Abstract A constrained interpolation profile (CIP)-based Cartesian grid method for strongly nonlinear wave–body interaction problems is presented and validated by a newly designed experiment, which is performed in a two- dimensional wave channel. In the experiment, a floating body that has a rectangular section shape is used. A superstructure is installed on the deck and a small floating- body freeboard is adopted in order to easily obtain water- on-deck phenomena. A forced oscillation test in heave and a wave–body interaction test are carried out. The numerical simulation is performed by the CIP-based Cartesian grid method, which is described in this paper. The CIP scheme is applied in the Cartesian grid-based flow solver. New improvements of the method include an interface-capturing method that applies the tangent of hyperbola for interface capturing (THINC) scheme and a virtual particle method for the floating body. The efficiency of the THINC scheme is shown by a dam-breaking computation. Numerical simulations on the experimental problem for both the forced oscillation test and the wave–body interaction test are carried out, and the results are compared to the mea- surements. All of the comparisons are reasonably good. It is shown, based on the numerical examples, that the present CIP-based Cartesian grid method is an accurate and effi- cient method for predicting strongly nonlinear wave–body interactions. Keywords CIP method  THINC scheme  Virtual particle method  Water on deck  Strongly nonlinear wave–body interaction 1 Introduction A Cartesian grid approach for predicting hydrodynamic loads associated with strongly nonlinear ship–wave inter- actions has been developed over a period of years in the Research Institute for Applied Mechanics (RIAM) at Kyushu University. The two- and three-dimensional development of the CFD code has been presented in pre- vious papers [1, 2]. The constrained interpolation profile (CIP) algorithm [3] was adopted as the base scheme to obtain a robust flow solver for the Cartesian grid approach. The Cartesian grid used for the numerical solution does not depend on the locations of the body boundary and the free surface. The use of such a grid makes the computation of strongly nonlinear problems with complicated free-surface deformation and violent body motion more efficient and robust than conventional body-fitted approaches. We call this numerical method the ‘‘CIP-based Cartesian grid method’’ in this paper. The free surface and the body boundary in the present numerical model are treated as immersed interfaces. As shown in Fig. 1, to recognize different phases we define a density function (or color function) / m , in which m = 1, 2, 3 denote the liquid, gas and solid phases, respectively. In each computational cell these density functions satisfy R/ m = 1.0. The moving free surface can be captured by the numerical solution of the equation for / 1 . Several types of CIP-based interface capturing methods have been applied for the free surface, such as original CIP and a CIP– C. Hu (&) RIAM, Kyushu University, 6-1 Kasuga-koen, Kasuga, Fukuoka 816-8580, Japan e-mail: hu@riam.kyushu-u.ac.jp M. Kashiwagi Graduate School of Engineering, Osaka University, 2-1 Yamada-oka, Suita, Osaka 565-0871, Japan 123 J Mar Sci Technol (2009) 14:200–213 DOI 10.1007/s00773-008-0031-4