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A numerical method was developed for solving potential flows for nonlinear free-surface wave problems with a fixed, small computational domain. The free-surface wave problem is solved as an initial value problem. The method of solving the free-surface wave problem couples the solution of the free-surface partial differential equations with the solution of the Laplace equation. The efficiency of the method is increased by solving the problem on a fixed, small computational domain, using an open boundary condition.
The implementation of the open boundary condition was studied by conducting a set of numerical experiments and by implementing the open boundary condition in the pressure-distribution problem at the outflow boundary, placed close to the pressure-distribution. The numerical experiments were conducted to systematically study the error in the calculation and to select an accurate numerical scheme.
Two methods were used to calculate accurate solutions of the free-surface equations and to control high frequency waves. The first method was to filter to control the high frequency waves. The second method was to use a damping scheme to solve the free-surface equations. The damping scheme was developed in three steps: modify the existing undamped schemes, incorporate artificial viscosity into the modified schemes by using upwind differencing, and, lastly, analyze the damping schemes to determine the effect of artificial viscosity on the solution of the free-surface equations. The damping scheme was more effective in calculating an accurate solution to the free-surface equations.
Unsteady and long time solutions were obtained for the pressure-distribution problem. At the higher Froude numbers, the nonlinearity of the wave-height solution was significant. An unsteady solution to the three-dimensional ship-wave problem was obtained.
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