Abstract
This chapter illustrates how to solve fully nonlinear water wave problems, using Eulerian–Lagrangian time stepping methods in conjunction with a desingularized approach to solve the mixed boundary value problem that arises at each time step. In the desingularized approach, the singularities generating the flow field are outside the fluid domain. This allows the singularity distribution to be replaced by isolated Rankine sources with the corresponding reduction in computational complexity and computer time. The desingularization method is robust in simulating the motions of floating bodies with complicated shapes, and it shows no difficulty in treating the body-free surface intersection point. For the method, no special treatment for the coefficient of the influence matrix is necessary. The stability of the desingularization method is better than that of the conventional boundary integral equation method. This method is promising for further application to floating structures with arbitrary shape undergoing arbitrary motion.
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