| Abstract | We are studying numerically the problem of generation and propagation of gravity long-crested waves in a tank containing an incompressible inviscid homogeneous fluid initially at rest with a horizontal free surface of finite extent and of infinite depth. A non-orthogonal curvilinear coordinate system, which follows the free surface is constructed and the full nonlinear kinematic and dynamic free surface boundary conditions are utilized in the algorithm. 'Wavemakers' are modeled using both the Dirichlet and Neumann lateral boundary conditions and a full comparison is given. Overall, the Dirichlet model was more stable than the Neumann model, with an upper limit of 0.08 using good resolution compared with the Neumann's maximum of 0.05. To place our work in perspective, see the review by Tsai and Yue (1996) - of the recent advances in computations of incompressible flows involving a fully nonlinear free surface. This paper advances the field of volume-discretization methods, using finite differences, by applying the relatively new method of waveform relaxation to reduce the 'computational dimensional' of the problem. This puts volume-discretization methods on a similar footing with boundary-discretization methods, which reduce the dimension of the problem by solving it on the boundary. |
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