A fourth-order compact finite volume scheme for fully nonlinear and weakly dispersive Boussinesq-type equations. Part II: Boundary conditions and validation

Abstract

This paper supplements the validation of the fourth-order compact finite volume Boussinesq-type model presented by Cienfuegos et al. (Int. J. Numer. Meth. Fluids 2006, in press). 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 Lynett et al. (Coastal Eng. 2002; 46:89-107), 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 Cienfuegos (Fifth International Symposium on Ocean Wave Measurement Analysis, Madrid, Spain, 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 Gaitonde et al. (Int. J. Numer Methods Engng 1999; 45:1849-1869) to damp out unphysical wavelengths, and the numerical robustness of the finite volume scheme are also discussed. Copyright (c) 2006 John Wiley & Sons, Ltd.