On the accuracy and efficiency of finite difference solutions for nonlinear waves

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We consider the relative accuracy and efficiency of low- and high-order finite difference discretizations of the exact potential flow problem for nonlinear water waves. The continuous differential operators are replaced by arbitrary order finite difference schemes on a structured but non-uniform grid. Time-integration is performed using a fourth-order Runge-Kutta scheme. The linear accuracy, stability and convergence properties of the method are analyzed in two-dimensions, and high-order schemes with a stretched vertical grid are found to be advantageous relative to second-order schemes on an even grid. Comparison with highly accurate periodic solutions shows that these conclusions carry over to nonlinear problems. The combination of non-uniform grid spacing in the vertical and fourth-order schemes is suggested as providing an optimal balance between accuracy and complexity for practical purposes.
Original languageEnglish
Title of host publicationHydrodynamics VII : Theory and Applications
EditorsP. Cassella, P. Cioffi
Number of pages711
Place of PublicationNaples, Italy
PublisherICHD 2006 Local Organizing Committee
Publication date2006
ISBN (Print)88-901174-4-3
Publication statusPublished - 2006
Event7th International Conference on Hydrodynamics - Ischia, Italy
Duration: 4 Oct 20066 Oct 2006
Conference number: 7


Conference7th International Conference on Hydrodynamics
Internet address

Cite this

Bingham, H. B. (2006). On the accuracy and efficiency of finite difference solutions for nonlinear waves. In P. Cassella, & P. Cioffi (Eds.), Hydrodynamics VII: Theory and Applications (Vol. 1, pp. 203-210). ICHD 2006 Local Organizing Committee.