Abstract
SUMMARYThis paper presents a comparison in terms of accuracy and efficiency between two fully nonlinear potential flow solvers for the solution of gravity wave propagation. One model is based on the high‐order spectral (HOS) method, whereas the second model is the high‐order finite difference model OceanWave3D. Although both models solve the nonlinear potential flow problem, they make use of two different approaches. The HOS model uses a modal expansion in the vertical direction to collapse the numerical solution to the two‐dimensional horizontal plane. On the other hand, the finite difference model simply directly solves the three‐dimensional problem. Both models have been well validated on standard test cases and shown to exhibit attractive convergence properties and an optimal scaling of the computational effort with increasing problem size. These two models are compared for solution of a typical problem: propagation of highly nonlinear periodic waves on a finite constant‐depth domain. The HOS model is found to be more efficient than OceanWave3D with a difference dependent on the level of accuracy needed as well as the wave steepness. Also, the higher the order of the finite difference schemes used in OceanWave3D, the closer the results come to the HOS model. Copyright © 2011 John Wiley & Sons, Ltd.
Highlights
The study of surface gravity waves is of major interest
In order to compare both models in terms of efficiency and accuracy from the previous results, one has to recall the details of each model: Firstly, as noted before, the number of points taken into account in the two models is different because the high-order spectral (HOS) method solves the problem on the free surface only, whereas in the OceanWave3D code, the vertical direction is discretized
The results will be strongly dependent on the choice of the order of the finite difference scheme and the DC or generalized minimal residual (GMRES) tolerance for OceanWave3D model and dependent on the order of nonlinearity M for the HOS model
Summary
The study of surface gravity waves (propagation, wave–wave interactions, etc.) is of major interest. The accurate description of wave fields is necessary in the ocean and naval engineering context to determine precisely the nonlinear wave loads acting on structures at sea, for instance. A wide variety of nonlinear wave models have been developed in the last decades to take care of this problem. Most of them were developed in the framework of potential flow theory considering that ocean wave propagation is essentially irrotational and inviscid (until the point of wave breaking). The computational effort required here restricts the solution to very small scales. The efficient and accurate solution of the fully nonlinear potential problem is still very challenging
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