| Abstract | A time-dependent numerical method, based upon an integral relation formulation, is presented for simulation of fluid flow problems that include a free surface. The method is first examined by applying it to unsteady propagation of waves of small amplitude. Propagation of a steep (nonlinear) wave is achieved by imposing an excitation potential at one of the vertical control boundaries. The exact nonlinear free surface conditions are treated by following free surface collocation points restricted to vertical motion. At the downstream boundary, Orlanski's radiation condition is adapted and is found to make the boundary sufficiently non-reflective. To preserve numerical stability, an appropriate smoothing in time and space is required at the upstream boundary, in conjunction with a smoothing on the free surface. Results are presented to demonstrate the efficacy of the method. This method is developed for applications to problems involving floating bodies in waves. |
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