Abstract
In order to simulate wave breaking process, air mass and bubbles entrained in water should be considered in calculation. In the present study, a numerical scheme is developed for wave breaking assuming an incompressible uni-phase flow with density varying between air and water. To satisfy the momentum conservation over the computational domain with large density variation, Navier-Stokes equation described in terms of momentum advection is employed as the governing equation. The advection terms of the momentum equation and advection equation for Density Value Method are solved by R-CIP method to minimize numerical diffusion. The results are compared with experimental results for a dam-break, bore and wave breaking on a slope. It is found that the model can reproduce bubbly areas due to wave breaking fairy well.References
Gong, X., S. Takagi, H. Huang, and Y. Matsumoto, 2007. A numerical study of mass transfer of ozone dissolution in bubble plumes with an Euler-Lagrange method, Chemical Engineering Science, 62, pp. 1081-1093.
Janosi, I. M., D. Jan, K. G. Szabo and T. Tel. 2004. Turbulent drag reduction in dam-break flows, Experiments in Fluids, 37, pp.219-229
Kawasaki, K., 1999. Numerical simulation of breaking and post-breaking wave deformation process around a submerged breakwater, Coastal Engineering Journal, Vol.41,Nos.3&4, pp.201-223.
Lubin, P., S. Vincent, S. Abadie, J. Caltagirone, 2006. Three-dimensional large eddy simulation of air entrainment under plunging breaking waves, Coastal Engineering, 53, pp. 631-655.
Ma, D., M. Liu, Y. Zu. and C. Tang, 2012. Two-dimensional volume of fluid simulation studies on single bubble formation and dynamics in bubble column, Chamical Engineering Science, 72, pp.61-77.
Miyata, H., A. Kanai, T. Kawamura and J. Park, 1996. Numerical simulation of three-dimensional breaking waves, Journal of Marine Science and Technology, 1:183-197.
Mori, N. and S Kakuno, 2008. Aeration and bubble measurements of coastal breaking waves, Fluid Dynamics Research, Volume 40, Issues 7-8, pp. 616-626.
Mutsuda, H. and T. Yasuda, 2000. Numerical Simulation of turbulent air-water mixing layer within surf-zone, Proceedings of 27th Int. Conf. on Coastal Eng., Sydney, pp.755-768.
Watanabe, Y., H. Saeki, 1999. Three-dimensional large eddy simulation of breaking waves, Coastal Engineering Journal, 41, 3-4, pp. 281-301.
Watanabe Y., Y. Niida, A. Saruwatari and H. Saeki, 2009. Stochastic models of entrainment and advection of air bubbles under jets, Journal of Coastal Engineering, JSCE, 56, pp. 6-10. (in Japanese)
Yabe, T., M. H. Mizoe, K. Takizawa, H. Moriki, H. Im and Y. Ogata, 2004. Higher-order schemes with CIP method and adaptive Soroban grid towards mesh-free scheme, Journal of Computational Physics, 194, pp. 57-77.