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.
|Title of host publication||Hydrodynamics VII : Theory and Applications|
|Editors||P. Cassella, P. Cioffi|
|Number of pages||711|
|Place of Publication||Naples, Italy|
|Publisher||ICHD 2006 Local Organizing Committee|
|Publication status||Published - 2006|
|Event||7th International Conference on Hydrodynamics - Ischia, Italy|
Duration: 4 Oct 2006 → 6 Oct 2006
Conference number: 7
|Conference||7th International Conference on Hydrodynamics|
|Period||04/10/2006 → 06/10/2006|
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.