Recent advances in the BEM modeling of nonlinear water waves

Chapter 4 in Boundary Element Applications in Fluid Mechanics (ed. H. Power), pps. 91-122. Advances in Fluid Mechanics Series. Computational Mechanics Publication, Southampton, UK 1995.

Abstract :  

Recent improvements to the fully nonlinear potential flow model by Grilli et al. are presented in the areas of : (i) higher-order free surface representation using the ``Mid Cubic Interpolation technique'' (ensuring continuity of both free surface slope and tangential gradient of field variables); (ii) numerical methods for quasi-singular integrations (an important problem for the computation of breaking waves in shallow water in computational domains with large aspect ratio); (iii) corner representation, continuity, and compatibility relationships (an important problem for wave generation by a numerical wavemaker in the model); (iv) node regridding and redistribution techniques (a necessary improvement for both resolving details of breaker jets and compensating for the ``node drift'' in nonlinear wave flows); (v) exact generation of nonlinear periodic (streamfunction) waves with zero-net-flux in the model (necessary to provide ``clean'' incident waves); and (vi) absorption of incident wave energy in the model with an adaptively calibrated ``absorbing beach'' (necessary for running long term computations of wave shoaling and breaking in shallow water).

Applications are presented for advanced nonlinear wave propagation problems that illustrate the newly improved features of the model.

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