Abstract
An overview is given of a discontinuous Galerkin finite element method for linear free surface water waves. The method uses an implicit time integration method which is unconditionally stable and does not suffer from the frequently encountered mesh dependent saw-tooth type instability at the free surface. The numerical discretization has minimal dissipation and small dispersion errors in the wave propagation. The algorithm is second order accurate in time and has an optimal rate of convergence O(hp+1) in the L2- norm, both in the potential and wave height, with p the polynomial order and h the mesh size. The numerical discretization is demonstrated with the simulation of water waves in a basin with a bump at the bottom.
Original language | English |
---|---|
Title of host publication | Computational Mechanics |
Subtitle of host publication | Proceedings of the Sixth World Congress on Computational Mechanics in conjunction with the Second Asian-Pacific Congress on Computational Mechanics, September 5-10, 2004, Beijing, China |
Editors | Z.H. Yao, M.W. Yuan, W.X. Zhong |
Place of Publication | Beijing |
Publisher | Tsinghua University Press |
Pages | 690-695 |
Number of pages | 6 |
ISBN (Print) | 9787302093435 |
Publication status | Published - 5 Sep 2004 |
Event | 6th World Congress on Computational Mechanics, WCCM 2004 - Beijing, China Duration: 5 Sep 2004 → 10 Sep 2004 Conference number: 6 |
Conference
Conference | 6th World Congress on Computational Mechanics, WCCM 2004 |
---|---|
Abbreviated title | WCCM VI |
Country/Territory | China |
City | Beijing |
Period | 5/09/04 → 10/09/04 |
Keywords
- Discontinuous Galerkin method
- Water waves
- Elliptic partial differential equations