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

    Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review


    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


    Dive into the research topics of 'On the accuracy and efficiency of finite difference solutions for nonlinear waves'. Together they form a unique fingerprint.

    Cite this