Free surface water wave 1-D LBGK predictions

International Journal of Computational Fluid Dynamics

Volumn 20, Issue 6, 2006, Pages 427-437

  Frandsen, J B ^a  

^a UNIVERSITY OF HAWAII   (United States)

Author keywords

LBGK model; Numerical wave tank; Tidal wave equations; Water waves

Indexed keywords

EID: 33751309409     PISSN: 10618562     EISSN: 10290257     Source Type: Journal    
DOI: 10.1080/10618560601000827     Document Type: Conference Paper

References (40)

1. Abramson, H.N., The dynamics of liquids in moving containers, 1966, Rep. SP 106, NASA.
2. Aidun, C.K., Lu, Y. and Ding, E.J., Direct analysis of particulate suspensions with inertia using discrete Boltzmann equation. J. Fluid Mech., 1998, 373, 287-311.
3. Benzi, R., Succi, S. and Vergassola, M., The lattice Boltzmann equation: theory and applications. Phys. Rep. (review section of Phys. Lett.), 1992, 222(3), 145-197.
4. Bhatnagar, P., Gross, E. and Krook, M.A., A model for collision processes in gases I: small amplitude process in charged and neutral one component systems. Phys. Rev. A, 1954, 94, 511-526.
5. Buick, J.M. and Created, C.A., Lattice Boltzmann modelling of interfacial gravity waves. Phys. Fluids, 2003, 10(6), 1490-1511.
6. Chen, S. and Doolen, G.D., Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech., 1998, 30(4), 329-364.
7. Crouse, B., Rank, E., Krafczyk, M. and Tölke, J., A LB-based approach for adaptive flow simulations. Int. J. Mod. Phys. B, 2003, 17(1 & 2), 109-112.
8. Deng, J.Q., Ghidaoui, M.S., Gray, W.G. and Xu, K., A Boltzmann-based mesoscopic model for contaminant transport in flow systems. Adv. Water Res., 2001, 24, 531-550.
9. Frandsen, J.B., Numerical predictions of tuned liquid tank structural systems. J. Fluids Struct., 2005, 20, 309-329.
10. Ghidaoui, M.S., Deng, J.Q., Gray, W.G. and Xu, K., A Boltzmann model for open channel flows. Int. J. Numer. Meth. Fluids, 2001, 35, 449-494.
11. Ginzburg, I. and Steiner, K., Lattice Boltzmann model for free-surface flow and its application to filling process in casting. J. Comput. Phys., 2003, 185, 61-99.
12. Ginzburg, I. and d'Humières, D., Multireflection boundary conditions for the lattice Bolzmann models. Phys, Rev. E 066614, 2003, 68(1), 1-30.
13. Guo, Z., Zheng, C. and Shi, B., Discrete lattice effects on the forcing term in the lattice Bolzmann method. Phys. Rev. E, 2002, 65(046308), 1-6.
14. He, X., Chen, S. and Zhang, R., A lattice Boltzmann scheme for incompressible multiphase flow and its application in simulation of Rayleigh-Taylor instability. J. Comput. Phys., 1999, 152, 642-663.
15. Hibberd, S. and Peregrine, D.H., Surf and run-up on a beach: a uniform bore. J. Fluid Mech., 1979, 95, 323-345.
16. Keller, H.B., Levine, D.A. and Whitham, G.B., Motion of a bore over a sloping beach. J. Fluid Mech., 1960, 7, 302-316.
17. Leveque, R.J., Finite Volume Methods for Hyperbolic Problems, 2002 (Wiley; New York).
18. Leveque, R.J., Chapter title. High resolution wave propagation numerical methods: shock capture methods. Advanced numerical models for simulating tsunami waves and runup. Advances in Coastal and Ocean Engineering, Vol. 10, 2006 (World Scientific: Singapore).
19. Li, Y. and Raichlen, F., Non-breaking and breaking solitary wave run-up. J. Fluid Mech., 2002, 456, 295-318.
20. Madsen, P.A., Bingham, H.B. and Liu, H., A new Boussinesq method for fully nonlinear waves from shallow to deep water. J. Fluid Mech., 2002, 462, 1-30.
21. McNamara, G.R. and Zanetti, G., Use of the Boltzmann equation to simulate lattice gas automata. Phys. Rev. Lett., 1988, 61(20), 2332-2335.
22. Mei, C.C., The Applied Dynamics of Ocean Surface Waves, p. 553, 1992 (World Scientific: Singapore).
23. Noble, R., Chen, S., Georgiadis, J. and Buckius, R., A consistent hydrodynamic boundary condition for the lattice Bolzmann method. Phys. Fluids, 1995, 7(1), 203-209.
24. Nourgaliev, R.R., Dinh, D.N., Theofanous, T.G. and Joseph, D., The lattice Boltzmann equation method: theoretical interpretation, numerics and implications. Int. J. Multiphase Flows, 2003, 29, 117-169.
25. Pan, C., Luo, L.-S. and Miller, C., An evaluation of lattice Bolzmann schemes for porous medium flow simulation. Comput. Fluids, 2006, 35(8-9), 898-909.
26. Pedersen, G., Chapter title. Modeling run-up with depth integrated equation models. Advanced numerical models for simulating tsunami waves and runup Advances in Coastal and Ocean Engineering, Vol. 10, 2006 (World Scientific: Singapore).
27. Rothman, D.H. and Zaleski, S., Lattice-Gas Cellular Automata. Simple Models of Complex Hydrodynamics, 1997 (Cambridge University Press: New York).
28. Salmon, R., The lattice Boltzmann method as a basis for ocean circulation modeling. J. Mar. Res., 1999, 57, 503-535.
29. Shen, M.C. and Meyer, R.E., Climb of a bore on a beach. Part 3: run-up. J. Fluid Mech., 1963, 16, 113-125.
30. Succi, S., The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, 2001 (Oxford University Press: Oxford).
31. Toro, E.F., Riemann Solvers and Numerical Methods for Fluid Dynamics, A Practical Introduction, pp. 168-171, 1999 (Springer: Berlin).
32. Toro, E.F., Shock-Capturing Methods for Free-Surface Shallow Flows, 2001 (Wiley: New York).
33. Van der Sman, R.G.M. and Ernst, M.H., Convection-diffusion lattice Boltzmann scheme for irregular lattices. J. Comput. Phys., 2000, 160, 766-782.
34. Vandiver, J.K. and Mitone, S., The effect of liquid storage tanks on the dynamic response of offshore platforms. J. Pet. Technol., 1979, 31(10), 1231-1240.
35. Wei, G., Kirby, J.T. and Sinha, A., Generation of waves in Boussinesq models using a function method. Coast. Eng., 1999, 36, 271-299.
36. Wu, G.X., Ma, Q.A. and Eatock Taylor, R., Numerical simulation of sloshing waves in a 3D tank based on a finite element method. Appl. Ocean Res., 1998, 20, 337-355.
37. Xu, K., A well-balanced gas-kinetic scheme for the shallow-water equations with source terms. J. Comput. Phys., 2002, 178, 533-562.
38. Yeh, H., Ghazali, A. and Marton, I., Experimental study of bore run-up. J. Fluid Mech., 1989, 206, 563-578.
39. Zhou, J.G., A lattice Boltzmann model for the shallow water equations with turbulence modeling. Int. J. Mod. Phys. C, 2002, 13(8), 1135-1150.
40. Zhou, J.G., Lattice Boltzmann Methods for Shallow Water Flows, 2004 (Springer: Berlin).