Numerical simulation of nonlinear wave-body problem based on desingularized Rankine source and mixed Euler-Lagrange method

Abstract

Rankine source method coupled with Mixed Euler-Lagrange (MEL) algorithm is developed to investigate wave-body problems. Under Euler specification a boundary-value problem is solved by placing fundamental singularities outside the computational domain and satisfying the boundary conditions at prescribed control points. At every time step, Lagrangian frame is applied to update the control points position during regridding process. A space increment method for source points distribution incorporating horizontal free surface source arrangement and vertical desingularized distance is developed and this method connects free surface panel to body panel size. By reducing the number of source points, this method significantly increases the computational efficiency. A single node scheme is implemented to treat intersection points. This scheme regards intersection points only as body panel ending points. The first source points on the free surface are placed away from the intersection points and generated wave is started from these source points rather than intersection points. During regridding process, body panel number keeps constant and panel size varies to match the variation of wetted body surface. In the process of repanelling the free surface, panels slide horizontally due to the variation of wetted body surface pushing them back and forth. After their horizontal positions are fixed, the source points follow the wave elevation and are located on the updated wave surface in the vertical direction. A least square based smoothing technique is developed to eliminate the "sawtooth" phenomenon occurred in the free surface updating for two-dimensional fully nonlinear problem. Both two- and three-dimensional forced body oscillatory motion problems are studied and extensive comparisons show a good agreement with published results. The methods developed are proved to be accurate, efficient and robust for wave-body problems.

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