Numerical modeling of water waves with the SPH method
Introduction
There are a variety of modern numerical methods to describe near breaking and breaking waves, including boundary element methods (e.g., Grilli et al., 2000), and methods taken from computational fluid dynamics: Direct Numerical Simulation (DNS; Lin and Liu, 1998, Chen et al., 1999), Reynolds Averaged Navier Stokes (RANS), and Large Eddy Simulation (LES) models (e.g. Wu (2004)). More recently the Smoothed Particle Hydrodynamics (SPH) method has been adapted from astrophysics into a number of fields, including free surface flows (Monaghan, 1994, Monaghan and Kos, 1999).
SPH offers a variety of advantages for fluid modeling, particularly those with a free surface. The Lagrangian method is meshfree; the equivalents of mesh points are the fluid particles moving with the flow. The free surface requires no special approaches, such as the volume-of-fluid method or a Lagrangian surface tracking. Furthermore, the method can treat rotational flows with vorticity and turbulence.
This paper presents a state-of-the-art review of improvements and enhancements we have made to the basic SPH methodology at The Johns Hopkins University (JHU). In the second part of the paper, we present examples of some of the basic applications that we have attempted to date.
Section snippets
Methodology
Smoothed Particle Hydrodynamics (SPH) can be considered as computing the trajectories of particles of fluid, which interact according to the Navier–Stokes equations. An alternative view is that the fluid domain is represented by nodal points that are scattered in space with no definable grid structure and move with the fluid. Each of these nodal points carry scalar information, density, pressure, velocity components, etc. To find the value of a particular quantity at an arbitrary point, x, we
Green water overtopping
Waves overtopping a ship or offshore platform deck can cause immense damage, e.g. Buchner, 1996a, Buchner, 1996b. An unbroken overtopping wave is referred to as ‘greenwater.’ Trulsen et al. (2002) have developed an irrotational model to examine overtopping, but it is clear that a model should include vorticity and conveniently model flow separation to be successful.
Gomez-Gesteira et al. (2005) used a two-dimensional SPH scheme to examine the overtopping of a flat plate, following the
Conclusions
The SPH technique, with its Lagrangian formulation, provides a methodology for the detailed examination of water waves. It is particularly suited to those cases where there is splash, or flow separation, as the determination of the free surface is not difficult. Improvements conducted at Johns Hopkins such as sub-grid scaling, Shephard filtering, and a new time stepping algorithm are detailed here.
For the examples shown here, realistic results are shown. The development of the JHU SPH model is
Acknowledgments
The authors gratefully acknowledge Office of Naval Research support through grant N00014-04-1-0089. Mr. Shan Zuo provided Fig. 3; thanks, Shan. Also, Dr. Andrea Panizzo (Universita degli Studi di Roma) and Dr. Moncho Gomez Gesteira (University of Vigo) have provided valuable support and assistance for this work.
References (34)
- et al.
Large eddy simulation of breaking waves
Coastal Engineering
(2001) - et al.
Numerical simulation of interfacial flows by smoothed particle hydrodynamics
Journal of Computational Physics
(2003) - et al.
Laboratory observations of green water overtopping a fixed deck
Ocean Engineering
(2002) - et al.
Green water overtopping analyzed with an SPH model
Ocean Engineering
(2005) On the problem of penetration in particle methods
Journal of Computational Physics
(1989)Simulating free surface flows with SPH
Journal of Computational Physics
(1994)- et al.
Modeling low Reynolds number incompressible flows using SPH
Journal of Computational Physics
(1997) - et al.
Large eddy simulation of turbulent flows in reversing systems
The influence of bow shape of FPSOs on drift forces and green water
The impact of green water on FPSO design
Two-dimensional Navier–Stokes simulation of breaking waves
Physics of Fluids
Using a 3D SPH method for wave impact on a tall structure
Journal of Waterway, Port, Coastal, and Ocean Engineering, Ocean Engineering
Sub-particle-scale model for the MPS method — Lagrangian flow model for hydraulic engineering
Computational Fluid Dynamics Journal
Numerical computation of 3D overturning waves
Numerical analysis of breaking waves using the moving particle semi-implicit method
International Journal of Numerical Methods in Fluids
Large-scale turbulence to facilitate sediment motion under spilling waves
Energy balance model for breaking solitary wave runup
Journal of Waterways, Ports, Coastal, and Ocean Engineering, ASCE
Cited by (0)
- 1
Present address: Federal Technical Institute of Lausanne, Switzerland.