Accuracy and Stability of Virtual Source Method for Numerical Simulations of Nonlinear Water Waves
- Omar Al-Tameemi (Plymouth University) | David I. Graham (Plymouth University) | Kurt Langfeld (University of Liverpool)
- Document ID
- International Society of Offshore and Polar Engineers
- The 28th International Ocean and Polar Engineering Conference, 10-15 June, Sapporo, Japan
- Publication Date
- Document Type
- Conference Paper
- 2018. International Society of Offshore and Polar Engineers
- accuracy, energy conservation, stability, boundary integral equation, Numerical wave tank (NWT)
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- 17 since 2007
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The virtual source method (VSM) developed by Langfeld et al., (2016) is based upon the integral equations derived by using Green's identity with Laplace's equation for the velocity potential. These authors presented preliminary results using the method to simulate standing waves. In this paper, we numerically model a non-linear standing wave by using the VSM to illustrate the energy and volume conservation. Analytical formulas are derived to compute the volume and potential energy while the kinetic energy is computed by numerical integration. Results are compared with both theory and boundary element method (BEM).
Many methods have been developed to study wave/structure interactions numerically by using the so called numerical wave tank (NWT). A comprehensive approach is to use ‘CFD’ methods to solve the full Navier-Stokes equations. For example Huang et al. (1998) developed a numerical model to simulate a nonlinear wave fields generated by a piston-type wavemaker by solving Navier-Stokes equations. Park et al (2001) developed the viscous 3D numerical wave tank to simulate regular, irregular and fully nonlinear multi-directional waves. However, a simple but common approach is the use of the fluid potential. Longuet-Higgins and Cokelet (1976) simulated an overturning wave using potential flow theory with a mixed Eulerian-Lagrangian method in combination with a boundary integral equation formulation. Wu and Taylor (1994) employed the finite element method for the nonlinear potential flow equation. Grilli et al. (2001) introduced the development of three-dimensional numerical wave tanks which contains an arbitrary bottom topography, sloping beach and the possibility to include wave makers. The nonlinear potential flow equation is solved with a combination of a boundary element method (BEM) and a mixed Eulerian-Lagrangian technique to compute the free surface motion. Recently, Langfeld et al. (2016) introduced the virtual source method (VSM) for solving free-surface potential flow problems and applied it to simulate standing waves in 2D and 3D.
|File Size||1 MB||Number of Pages||8|