A fourth-order compact finite volume scheme for fully nonlinear and weakly dispersive Boussinesq-type equations. II: Boundary conditions and validation. (English) Zbl 1370.76090
Summary: This paper supplements the validation of the fourth-order compact finite volume Boussinesq-type model presented by the first author et al. [ibid. 51, No. 11, 1217–1253 (2006; Zbl 1158.76361)]. We discuss several issues related to the application of the model for realistic wave propagation problems where boundary conditions and uneven bathymetries must be considered. We implement a moving shoreline boundary condition following the lines given by P. J. Lynettet al. [“Modeling wave runup with depth-integrated equations”, Coast. Eng. 46, No. 2, 89–107 (2002; doi:10.1016/s0378-3839(02)00043-1)], while an absorbing-generating seaward boundary and an impermeable vertical wall boundary are approximated using a characteristic decomposition of the Serre equations. Using several benchmark tests, both numerical and experimental, we show that the new finite volume model is able to correctly describe nonlinear wave processes from shallow waters and up to wavelengths which correspond to the theoretical deep water limit. The results compare favourably with those reported using former fully nonlinear and weakly dispersive Boussinesq-type solvers even when time integration is conducted with Courant numbers greater than 1.0. Furthermore, excellent nonlinear performance is observed when numerical computations are compared with several experimental tests on solitary waves shoaling over planar beaches up to breaking. A preliminary test including the wave-breaking parameterization described by the first author et al. [“A new wave-breaking parametrization for Boussinesq-type equations”, in: B. Edge and J. C. Santàs (eds.), Proceedings of the 5th International symposium WAVES 2005 (53). Madrid (2005)]. shows that the Boussinesq model can be extended to deal with surf zone waves. Finally, practical aspects related to the application of a high-order implicit filter as given by D. V. Gaitonde et al. [Int. J. Numer. Methods Eng. 45, No. 12, 1849–1869 (1999; Zbl 0959.65103)] to damp out unphysical wavelengths, and the numerical robustness of the finite volume scheme are also discussed.
MSC:
| 76M12 | Finite volume methods applied to problems in fluid mechanics |
| 76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |
Keywords:
Boussinesq-type equations; Serre equations; finite volume method; compact schemes; boundary conditionsReferences:
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