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

Journal Article · Wed Apr 01 04:00:00 EDT 2009 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2008.11.028· OSTI ID:21167768

Bingham, H B; Lindberg, O ^[1]

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1. Technical University of Denmark, Department of Mechanical Engineering, Lyngby (Denmark)

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.

• OSTI ID: 21167768
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 6 Vol. 228; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ACCURACY
BOUNDARY CONDITIONS
ENERGY CONSERVATION
FINITE DIFFERENCE METHOD
NONLINEAR PROBLEMS
POTENTIAL FLOW
WATER WAVES