This paper describes a finite element method applied to a nonlinear free surface flow problem for a ship moving in three dimensions. The physical model is taken to simulate the towing tank experimental conditions. The exact nonlinear free-surface flow problem formulated by an initial/boundary value problem is replaced by an equivalent weak formulation. The same problem was considered earlier by Bai, et. al. [1] where some irregularities were observed in the downstream waves and a transom stern ship geometry could not be treated. In the present paper, specifically, three improvements are made from the earlier work. The first improvement is the introduction of the 5-point Chebyshev filtering scheme which eliminates the irregular and saw-toothed waves in the downstream. The second improvement is that now we can treat a transom stern ship geometry. The third improvement is the introduction of a new boundary condition to simulate a dry bottom behind a transom stern ship which is stretched from the free surface to the bottom at a high Froude number. Computations are made for two models. The first model is tested for the generation of the solitons in the upstream and smooth waves in the downstream. The second model is used to compute the generation of a dry bottom behind a transom stern which is one of highly nonlinear phenomena. The results of the first model show a good agreement with previous results for the generation of the solitons. The results of the second model also show a good agreement with the preliminary experimental observation for a dry-bottom, which will be reported in near future. The numerical simulation of the second model can be applied to the local flow behind a sail of a submarine in cruise, a sloshing problem in LNG tankers, and a dam breaking problem. Both computed models are assumed to be in shallow water for simplicity. However, the present numerical method can treat arbitrary water-depth and practical ship geometries.
Fully implicit time discretization for a free surface flow problem
