For the simulation of the nonlinear wave propagation in coastal areas with complex boundaries,a numerical model is developed in curvilinear coordinates. In the model,the Boussinesq-type equations including the dissipation terms are employed as the governing equations. In the present model,the dependent variables of the transformed equations are the free surface elevation and the utility velocity variables,instead of the usual primitive velocity variables. The introduction of utility velocity variables which are the products of the contravariant components of the velocity vector and the Jacobi matrix can make the transformed equations relatively concise,the treatment of lateral boundary conditions easier and the development of the program simpler. The predictor-corrector method and five-point finite-difference scheme are employed to discretize the time derivatives and the spatial ones,respectively. The numerical model is tested for three cases. It is found that the numerical results are in good agreement with the analytical results and experimental data.
If the upstream boundary conditions are prescribed based on the incident wave only,the time-dependent numerical models cannot effectively simulate the wave field when the physical or spurious reflected waves become significant.This paper describes carefully an approach to specifying the incident wave boundary conditions combined with a set sponge layer to absorb the reflected waves towards the incident boundary.Incorporated into a time-dependent numerical model,whose governing equations are the Boussinesq-type ones,the effectiveness of the approach is studied in detail.The general boundary conditions,describing the down-wave boundary conditions are also generalized to the case of random waves.The numerical model is in detail examined.The test cases include both the normal one-dimensional incident regular or random waves and the two-dimensional oblique incident regular waves.The calculated results show that the present approach is effective on damping the reflected waves towards the incident wave boundary.
On the basis of the new type Boussinesq equations (Madsen et al.,2002),a set of equations explicitly including the effects of currents on waves are derived.A numerical implementation of the present equations in one dimension is described.The numerical model is tested for wave propagation in a wave flume of uniform depth with current present.The present numerical results are compared with those of other researchers.It is validated that the present numerical model can reasonably reflect the nonlinear influences of currents on waves.Moreover,the effects of inputting different incident boundary conditions on the calculated results are studied.
A new type Boussinesq model is proposed and applied for wave propagation in a wave flume of uniform depth and over a submerged bar with current present or absent,respectively.Firstly,for the propagation of monochromatic incident wave with current absent,the Boussinesq model is tested in its complete form,and in a form without the introduction of utility velocity variables.It is validated that the introduction of utility velocity variables can improve the characteristics of velocity field,dispersion and nonlinearity.Both versions of the Boussinesq models are of higher accuracy than the fully-nonlinear fourth-order model,which is one of the best forms among the existing traditional Boussinesq models that do not incorporate breaking mechanism in one dimension.Secondly,the Boussinesq model in its complete form is applied to simulating the propagation of bichromatic incident waves with current present or absent,respectively,and the modeled results are compared to the analytical ones or the experimental ones.The modeled results are reasonable in the case of inputting bichromatic incident waves with the strong opposing current present.
