Computation of Nonlinear Gravity Waves by a Desingularized Boundary IntegralMethod

摘要

A desingularized boundary integral equation method combined with an Eulerian-Lagrangian time-stepping technique is developed for nonlinear gravity wave problems. The desingularization distance between the boundary and the sources is related to the local mesh size to ensure convergence. Tests for some simple problems show that desingularization significantly reduces the computer time required to compute the influence matrix of the resulting algebraic system. The algebraic system is still adequately well-conditioned to allow fast iterative solutions. Accurate solutions can be obtained for a large range of desingularization distances on the order of the mesh size. Several nonlinear water wave problems a-re then investigated. The first problem considers upstream runaway solitons due to a disturbance moving near critical speed in two-dimensional shallow water. Results from the desingularized method with the fully nonlinear free surface boundary condition agree well to those using the fKdV model for weak disturbances. The fully nonlinear model predicts larger solitons than the fKdV model for strong disturbances and also predicts the breaking of waves for some stronger disturbances.