In this paper, we focus on the implementation and verification of an extended Boussinesq model for surf zone hydrodynamics in two horizontal dimensions. The time-domain numerical model is based on the fully nonlinear Boussinesq equations. As described in Part I of this two-part paper, the energy dissipation due to wave breaking is modeled by introducing an eddy viscosity term into the momentum ...

In this paper a new set of Boussinesq wave equations with improved linear dispersion properties is proposed for extending its application to deeper water without having its mathematical form changed. The improvements are due to the combination of a generalized set of Boussinesq wave equations expressed in terms of any velocity, with additional dispersive terms obtained by invoking the linear sh...

A coupled Boussinesq-boundary integral method is developed to simulate nonlinear water wave interaction with structures consisting of multiple layers with different physical and hydraulic characteristics. The flow field in the water region is modeled with a modified set of Boussinesq-type equations, with additional terms to account for the flow of water into/out of the porous region. The equati...

We use extended mapping method and auxiliary equation method for finding new periodic wave solutions of nonlinear evolution equations in mathematical physics, and we obtain some new periodic wave solution for the Boussinesq system and the coupled KdV equations. This method is more powerful and will be used in further works to establish more entirely new solutions for other kinds of nonlinear pa...

By using the long-wave approximation, a system of coupled evolution equations for the bulk velocity and the surface perturbations of a BénardMarangoni system is obtained. It includes nonlinearity, dispersion and dissipation, and it can be interpreted as a dissipative generalization of the usual Boussinesq system of equations. As a particular case, a strictly dissipative version of the Boussines...

A set of optimum parameter a is obtained to evaluate the linear dispersion and shoaling properties in the extended Boussinesq equations of Madsen and Sørensen (1992), Nwogu (1993), and Chen and Liu (1995). Optimum a values are determined to produce minimal errors in each wave property of phase velocity, group velocity, or shoaling coefficient relative to the analytical one given by the Stokes w...

In this work, recently deduced generalized Kudryashov method is applied to the variant Boussinesq equations, and the (2 + 1)-dimensional breaking soliton equations. As a result a range of qualitative explicit exact traveling wave solutions are deduced for these equations, which motivates us to develop, in the near future, a new approach to obtain unsteady solutions of autonomous nonlinear evolu...

The   ) ( exp    -expansion method is a promising method for finding exact traveling wave solutions to nonlinear evolution equations in physical sciences. In this article, we use the   ) ( exp    -expansion method to find the exact solutions for the nonlinear Zakharov-Kuznetsov-Benjamin-Bona-Mahony equation and the good Boussinesq equations. Many solitary wave solutions are formally d...

Undular bores and shocks generated by dam-break flows or tsunamis are examined considering nonhydrostatic pressure and dispersive effects in oneand two-horizontal-dimensional space. The fully nonlinear Boussinesq-type equations based on a weakly nonhydrostatic pressure assumption are chosen as the governing equations. The equation set is solved by a fourth-order accurate finite-volume method wi...

Dual Scattering Channel schemes generalise Johns’ TLM algorithm and replace the latter in situations where the transmission line picture of wave propagation fails. This is notoriously the case in applications to fluid dynamics, for instance. In this paper, a DSC numerical solution of the Oberbeck-Boussinesq equations is presented, which approximate the Navier-Stokes equations for viscous quasi ...