Applications of boundary integral equation methods for two‐dimensional non‐linear water wave problems

Abstract

On the basis of the integral equation approach, numerical algorithms for solving non-linear water wave problem are presented. The free surface flow is assumed to be irrotational. Two different Green functions are used in the integral equations. The non-linear free-surface boundary conditions are treated by a timestepping Lagrangian technique. Several numerical examples are given, including permanent periodic waves, overturning progressive waves, breaking standing waves and sloshing problems.

Numerical simulation of the three‐dimensional sloshing problem by boundary element method

“…7. The result of the case, ay=5.5 rad/sec, is very consistent with that of the two-dimensional computation by Liu et al (1992). In this case, the wave amplitude at the wall increases almost linearly.…”

“…(7)) for practical engineering applications (Nakayama and Washizu, 1981). The other forced frequency, <jfy=5.0 rad/sec, is far away from the resonance frequency, so the amplitude of the free surface wave is more calming and a "surf beat" phenomenon appears (Liu et al, 1992). Fig.…”

High-Order Schemes in Boundary Element Methods for Transient Non-Linear Free Surface Problems

“…This approach, developed first by Dold and Peregrine, 2,3 has been successfully used by several authors to treat non-linear water wave problems. 11,12,14 However, they have limited their studies to the gravitational case without capillary effects and restricted the computations to second-order schemes in time integration coupled with a linear approximation in the BEM solver. Since very accurate results are sometimes required, we devoted our study to the feasibility of an extension of this approach to higher orders.…”

Wave kinematic fields from the boundary integral method

“…The ÿrst, algorithm A, is broadly representative of common ÿnite element practice [3,4] for the boundary integral method in water waves, except that the element integrations are completed analytically rather than numerically. Detailed evaluation in the context of moderately extreme steady water waves demonstrates the utility of this common approach throughout the interior of the solution domain.…”