MULTIPHASE MODELING OF WAVE PROPAGATION OVER SEMICIRCULAR OBSTACLES USING WENO AND LEVEL SET METHODS

Tamer Kasem, Jun Sasaki

Abstract


Wave propagation over a semicircular obstacle is studied. This problem is related to the design of semicircular breakwaters. These breakwaters are expected to have enhanced stability and were constructed in various places in China. Enhanced numerical modeling is done taking viscosity into account. The fifth order space accurate weighted essentially non-oscillatory (WENO) method is used to discretize the convection terms. As a result accurate results are obtained using simple options (uniform Cartesian grid, level set method). Wave generation is done using a numerical piston wave maker that is analogous to the real experiment. The model results are compared with free surface visualization and pressure measurements. Various features of the problem including wave drag and the flow field are revealed.

Keywords


Semicircular breakwater; Numerical model; WENO; Visualization

References


Anderson, D, J Tannehill, and R Pletcher. 1984. Computational Fluid Mechanics and Heat Transfer, Taylor & Francis, 816pp.

Dean, R., and R. Dalrymple. 1984. Water Wave Mechanics for Engineers and Scientists, Prentice-Hall, 353 pp.

Dong, C., and C. Huang. 2004. Generation and propagation of water waves in a two-dimensional numerical viscous wave flume, Journal of Waterway, Port, Coastal & Ocean Engineering, 130, 143-153. http://dx.doi.org/10.1061/(ASCE)0733-950X(2004)130:3(143)

Goda, Y. 1985. Random Seas and Design of Maritime Structures, University of Tokyo Press, 323 pp.

Gresho, P. 1991. Incompressible Fluid Dynamics: Some Fundamental Formulation Issues, Annual Review of Fluid Mechanics, 23, 413-453. http://dx.doi.org/10.1146/annurev.fl.23.010191.002213

Gresho, P., and R. Sani. 1987. On pressure boundary conditions for the incompressible Navier-Stokes equations, International Journal for Numerical Methods in Fluids, 7, 1111-1145. http://dx.doi.org/10.1002/fld.1650071008

Hughes, S. 1993. Physical Models and laboratory Techniques in Coastal Engineering, World Scientific, 550 pp.

Interim Development Committee of a Numerical Wave Flume for Maritime Structure Design. 2001. Numerical Wave Flume Theory and Development, Coastal Development Institute of Technology –Japan, (in Japanese).

Isobe, M., S. Takahashi,, S. Yu, T. Sakakiyama,, K. Fujima, K. Kawasaki,, Q. Jiang, M. Akiyama, and H. Oyama. 1999. Interim development of a numerical wave flume for maritime structure design, Proceedings of Civil Engineering in the Ocean, JSCE, 321-326, (in Japanese).

Lin, P., and P. Liu. 1998. A numerical study of breaking waves in the surf zone, Journal of Fluid Mechanics, 359, 239-264. http://dx.doi.org/10.1017/S002211209700846X

Lin, P., and P. Liu. 1999. Internal Wave-Maker for Navier-Stokes Equations Models, Journal of Waterway, Port, Coastal & Ocean Engineering, 125, 207-215. http://dx.doi.org/10.1061/(ASCE)0733-950X(1999)125:4(207)

Massel, R. 1996. Ocean Surface Waves: Their Physics and Prediction, World Scientific, 491 pp. PMid:9191511

Reeve, D., A. Chadwick, and C. Fleming. 2004. Coastal Engineering, Processes, Theory and Design Practice, Spon Press, 416 pp.

Sani, R., J. Shen, O. Pironneau, and P. Gresho. 2006. Pressure boundary condition for the timedependent incompressible Navier–Stokes equations, International Journal for Numerical Methods in Fluids, 50, 673-682. http://dx.doi.org/10.1002/fld.1062

Sasajima, H., T. Koizuka, H. Sasayama, Y. Niidome, and T. Fujimoto. 1994. Field demonstration test on a semi-circular breakwater, Proceedings of the International Conference on Hydro-Technical Engineering for Port & Harbor Construction, HYDRO-PORT'94, Yokosuka, Japan, 593-615.

Scardovelli, R., and S. Zaleski. 1999. Direct numerical simulation of free-surface and interfacial flow, Annual Review of Fluid Mechanics, 31, 567-603. http://dx.doi.org/10.1146/annurev.fluid.31.1.567

Sethian, J., and P. Smereka. 2003. Level set methods for fluid interfaces, Annual Review of Fluid Mechanics, 35, 341-372. http://dx.doi.org/10.1146/annurev.fluid.35.101101.161105

Shu, C. 1998. Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws, Lecture Notes in Mathematics, Vol. 1697, in Advanced Numerical Approximation of Nonlinear Hyperbolic Equations, edited by A Quarteroni, 325-432. http://dx.doi.org/10.1007/BFb0096355

Sussman, M., P. Smereka, and S. Osher. 1994. A level set approach for computing solutions to incompressible two-phase flow, Journal of Computational Physics, 114, 146-159. http://dx.doi.org/10.1006/jcph.1994.1155

Tamer, K., and J. Sasaki. 2010. Multiphase modeling of wave propagation over submerged obstacles using weno and level set methods, Coastal Engineering Journal, (in press).

Troch, P., and J. De-Rouk. 1998. Development of two-dimensional numerical wave flume for wave interaction with rubble mound breakwaters, Proceedings of the 26th International Conference on Coastal Engineering, ASCE, 1638-1649.

Troch, P., and J. De-Rouk. 1999. An active wave generating-absorbing boundary condition for VOF type numerical model, Coastal Engineering, 38, 223-247. http://dx.doi.org/10.1016/S0378-3839(99)00051-4

Yabe, T., T. Ishikawa, P. Wang, T. Aoki, Y. Kadota, and F. Ikeda. 1991. A universal solver for hyperbolic equations by cubic-polynomial interpolation II. Two- and three-dimensional solvers, Computer Physics Communications, 66, 233-242. http://dx.doi.org/10.1016/0010-4655(91)90072-S

Yuan, D., and J. Tao. 2003. Wave forces on submerged, alternately submerged, and emerged semicircular breakwaters, Coastal Engineering, 48, 75-93. http://dx.doi.org/10.1016/S0378-3839(02)00169-2

Zhuang, F., and J. Lee. 1996. A Viscous Rotational Model for Wave Overtopping over Marine Structure, Proceedings of the 25th International Conference on Coastal Engineering, Orlando, Florida: ASCE, 2178-2191.


Full Text: PDF

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.