Proc. 26 th Int. Workshop on Water Waves and Floating Bodies, Athens, April 2011 1 Application of Chimera grid concept to simulation of the free-surface boundary condition Shukui LIU 1, a , Apostolos PAPANIKOLAOU 1, b 1 Address of authors: Ship Design Laboratory, National Technical University of Athens, Athens, Greece a liushukui@deslab.ntua.gr, b papa@deslab.ntua.gr 1. INTRODUCTION Due to the highly oscillatory behavior of the time domain transient Green function, it proves intricate to apply directly the Time Domain Green Function method (TDGF) to seakeeping problems of floating bodies. Though some improved numerical scheme for the fundamental problem has been developed in recent time [2] , no significant development of this approach could be noted. On the other hand, hybrid-type methods were more widely studied and successfully applied to many free surface problems [3,7,9,11] . Commonly used hybrid methods are a combination of a time-domain transient Green function method [10] for the outer domain and a Rankine source method for the inner domain of the fluid. Herein, the quite robust Rankine source method is applied in the inner domain to find the dominant velocity potential equation, while the transient Green function method is used in the outer domain to obtain matching relationships for the velocity potential and its normal derivative between the inner and outer domain solution. In this approach, the free surface needs to be numerically simulated, whereas the captured free surface area needs to be very large for specific problems and the panel size needs to be adjusted to the specific demands of numerical stability. Thus, there is an inherent need for efficient numerical schemes for the treatment of the free surface condition. In this paper, we introduce the Chimera grid concept to efficiently simulate the free surface and to demonstrate its application by use of a hybrid method to the wave resistance problem of a ship-like hull form. 2. Free-surface condition The linearized free-surface condition (at z=0) can be expressed in an earth-bound (inertial) coordinate system, with the z axis positive upwards, as: 2 2 0 g t z       (1) This expression can be rewritten as: 2 2 g t z      Integrating the above equation with respect to time t twice and taking into account the initial conditions, we will get the following expression:     0 , t p g t d n         (2) This formulation, first developed by Wang [5] , is very simple and also proved to be a robust free-surface simulator [8] . It should be noted that during the development of the above expression, the integration is done with respect to time from moment 0 to moment t and the initial condition is set as 0 0 0 t t t        . This is valid only for the area that is free from disturbance/occupation by the moving hull. For the area that is in the wake of the hull or the area which is occupied by the hull at the very beginning but gradually becomes free, the free surface condition is expressed as following:             0 0 0 0 , , , , t t t p p pt pt t t g t d n                   (3)