WAVE BREAKING USING A ROLLER APPROACH IN A HYBRID FINITE-VOLUME FINITE-DIFFERENCE BOUSSINESQ-TYPE MODEL
ICCE 2014 Cover Image
PDF

Keywords

Boussinesq equations
Finite-volume finite-difference
Wave breaking

How to Cite

Tatlock, B., Briganti, R., & Musumeci, R. E. (2014). WAVE BREAKING USING A ROLLER APPROACH IN A HYBRID FINITE-VOLUME FINITE-DIFFERENCE BOUSSINESQ-TYPE MODEL. Coastal Engineering Proceedings, 1(34), waves.13. https://doi.org/10.9753/icce.v34.waves.13

Abstract

A new scheme implementing a roller approach into a hybrid finite-volume finite-difference Boussinesq-type model is presented. The relevant mathematics are outlined and a numerical solver is described. Predictions obtained from the model are validated against physical observations, demonstrating the capabilities of the scheme to replicate the complex hydrodynamic processes that occur during wave breaking. The benefits of both the hybrid scheme and the roller approach are discussed. The results illustrate the feasibility of modelling the breaking process with a rotational roller method in a finite-volume finite-difference scheme and show the obtainable accuracies. Finally, further tests and improvements to the model are proposed.
https://doi.org/10.9753/icce.v34.waves.13
PDF

References

Briganti, R., R. E. Musumeci, G. Bellotti, M. Brocchini, and E. Foti (2004). "Boussinesq modeling of breaking waves: Description of turbulence†. Journal of Geophysical Research 109.C07015, pp. 1-17. Brocchini, M. (2013). "A reasoned overview on Boussinesq-type models: the interplay between physics, mathematics and numerics†. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science 469.2160.

Cox, D. T., N. Kobayashi, and A. Okayasu (1995). Experimental and numerical modeling of surf zone hydrodynamics. CACR-95-97. University of Delaware: Center for Applied Coastal Research.

Cox, D. T., N. Kobayashi, and A. Okayasu (1996). "Bottom shear stress in the surf zone†. Journal of Geophysical Research: Oceans 101.C6, pp. 14337-14348.

Hansen, J. B. and I. A. Svendsen (1979). Regular waves in shoaling water: experimental data. Series paper No. 21. Technical University of Denmark: Institute of Hydrodynamics and Hydraulic Engineering.

Harten, A., P. D. Lax, and B. van Leer (1983). "On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws†. SIAM Review 25.1, pp. 35-61.

Leer, B. van (1984). "On the Relation Between the Upwind-Differencing Schemes of Godunov, Engquist-Osher and Roe†. SIAM Journal on Scientific and Statistical Computing 5.1, pp. 1-20.

Musumeci, R. E., I. A. Svendsen, and J. Veeramony (2005). "The flow in the surf zone: a fully nonlinear Boussinesq-type of approach†. Coastal Engineering 52.7, pp. 565-598.

Shi, F., J. T. Kirby, J. C. Harris, J. D. Geiman, and S. T. Grilli (2012). "A high-order adaptive time-stepping TVD solver for Boussinesq modeling of breaking waves and coastal inundation†. Ocean Modelling 43-44, pp. 36-51.

Tonelli, M. and M. Petti (2009). "Hybrid finite volume - finite difference scheme for 2DH improved Boussinesq equations†. Coastal Engineering 56.5-6, pp. 609-620.

Toro, E. F. (2009). Riemann Solvers and Numerical Methods for Fluid Dynamics. A Practical Introduction. 3rd ed. Springer-Verlag.

Veeramony, J. and I. A. Svendsen (2000). "The flow in surf-zone waves†. Coastal Engineering 39.2-4, pp. 93-122.

Wei, G., J. T. Kirby, and A. Sinha (1999). "Generation of waves in Boussinesq models using a source function method†. Coastal Engineering 36.4, pp. 271-299.

Yamamoto, S., S. Kano, and H. Daiguji (1998). "An efficient CFD approach for simulating unsteady hypersonic shock-shock interference flows†. Computers & Fluids 27.5-6, pp. 571-580.

Authors retain copyright and grant the Proceedings right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this Proceedings.