An efficient flexible-order model for 3D nonlinear water waves

The flexible-order, finite difference based fully nonlinear potential flow model described in [H.B. Bingham, H. Zhang, On the accuracy of finite difference solutions for nonlinear water waves, J. Eng. Math. 58 (2007) 211–228] is extended to three dimensions (3D). In order to obtain an optimal scalin...

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Bibliographic Details
Published in:Journal of computational physics 2009-04, Vol.228 (6), p.2100-2118
Main Authors: Engsig-Karup, A.P., Bingham, H.B., Lindberg, O.
Format: Article
Language:English
Subjects:
ACCURACY
BOUNDARY CONDITIONS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Computational techniques
ENERGY CONSERVATION
Exact sciences and technology
FINITE DIFFERENCE METHOD
Finite differences
Mathematical methods in physics
Multigrid
NONLINEAR PROBLEMS
Nonlinear waves
Ocean engineering
Physics
POTENTIAL FLOW
Time domain
WATER WAVES
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Summary:The flexible-order, finite difference based fully nonlinear potential flow model described in [H.B. Bingham, H. Zhang, On the accuracy of finite difference solutions for nonlinear water waves, J. Eng. Math. 58 (2007) 211–228] is extended to three dimensions (3D). In order to obtain an optimal scaling of the solution effort multigrid is employed to precondition a GMRES iterative solution of the discretized Laplace problem. A robust multigrid method based on Gauss–Seidel smoothing is found to require special treatment of the boundary conditions along solid boundaries, and in particular on the sea bottom. A new discretization scheme using one layer of grid points outside the fluid domain is presented and shown to provide convergent solutions over the full physical and discrete parameter space of interest. Linear analysis of the fundamental properties of the scheme with respect to accuracy, robustness and energy conservation are presented together with demonstrations of grid independent iteration count and optimal scaling of the solution effort. Calculations are made for 3D nonlinear wave problems for steep nonlinear waves and a shoaling problem which show good agreement with experimental measurements and other calculations from the literature.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2008.11.028