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On nonlinear free surface potential flow by a Bubnov-Galerkin formulation in space and a semi-lagrangian semi-implicit scheme in time Allievi, Alejandro


The potential flow initial-boundary value problem describing fluid-structure interaction with fully nonlinear free surface boundary conditions has been studied using a mixed Lagrangian-Eulerian formulation. The boundary-value problem has been solved in the physical domain by means of a Bubnov-Galerkin formulation of the Laplace equation. The initialvalue problem related to the behavior of some of the moving boundaries has been discretized using various numerical techniques. Among these is a series of predictor-corrector methods. These methodologies proved to require considerable numerical smoothing to maintain stability of the numerical scheme. In turn, dissipation led to inaccuracies in the solution of the problem. In order to avoid this negative effect, a semi-implicit semi-Lagrangian two-time level iterative scheme that is almost free from smoothing has been developed. A Bubnov-Galerkin formulation of an elliptic system for the generation of boundary fitted curvilinear coordinates has been used. When solved iteratively, this method provides orthogonal meshes of very good characteristics for both symmetric and non-symmetric domains. Previous publications concluded that the present system was inadequate for non-symmetric regions leading to lack of convergence in the iterative process. Solutions described in this work show that this limitation has been overcome. Fluid responses to periodic excitation of surface-piercing and submerged bodies have been calculated. Both linear and nonlinear cases show agreement with published results. Very low total energy/work error has been obtained which demonstrates accuracy, good stability and convergence characteristics of the numerical scheme. The impulsive response of tanks of various shapes has also been simulated. Resulting natural frequencies show good agreement with available data. A slender body representation of the flow around a hull advancing with forward speed in otherwise calm water has also been simulated. Numerical calculations of a number of quantities of engineering interest are presented for different length Froude numbers. Results compare favorably with experimental data.

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