Abstract
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 language | English |
|---|---|
| Title of host publication | Hydrodynamics VII : Theory and Applications |
| Editors | P. Cassella, P. Cioffi |
| Number of pages | 711 |
| Volume | 1 |
| Place of Publication | Naples, Italy |
| Publisher | ICHD 2006 Local Organizing Committee |
| Publication date | 2006 |
| Pages | 203-210 |
| ISBN (Print) | 88-901174-4-3 |
| Publication status | Published - 2006 |
| Event | 7th International Conference on Hydrodynamics - Ischia, Italy Duration: 4 Oct 2006 → 6 Oct 2006 Conference number: 7 http://www.ichd2006.unina.it/callfor%20papers.htm |
Conference
| Conference | 7th International Conference on Hydrodynamics |
|---|---|
| Number | 7 |
| Country/Territory | Italy |
| City | Ischia |
| Period | 04/10/2006 → 06/10/2006 |
| Internet address |