This study deals with the general numerical model to simulate the two-dimensional tidal flow, flooding wave (long wave) and shallow water waves (short wave). The foundational model is based on nonlinear Boussinesq equ...This study deals with the general numerical model to simulate the two-dimensional tidal flow, flooding wave (long wave) and shallow water waves (short wave). The foundational model is based on nonlinear Boussinesq equations. Numerical method for modelling the short waves is investigated in detail. The forces, such as Coriolis forces, wind stress, atmosphere and bottom friction, are considered. A two-dimensional implicit difference scheme of Boussinesq equations is proposed. The low-reflection outflow open boundary is suggested. By means of this model,both velocity fields of circulation current in a channel with step expansion and the wave diffraction behind a semi-infinite breakwater are computed, and the results are satisfactory.展开更多
Nonlinear acoustic propagation generated by a piston in a finite horn is numerically studied. A quasi-one-dimensional nonlinear model with varying cross-section uses high-order low-dispersion numerical schemes to solv...Nonlinear acoustic propagation generated by a piston in a finite horn is numerically studied. A quasi-one-dimensional nonlinear model with varying cross-section uses high-order low-dispersion numerical schemes to solve the governing equation. Because of the nonlinear wave distortion and reflected sound waves at the mouth, broadband time-domain impedance boundary conditions are employed. The impedance approximation can be optimized to identify the complex-conjugate pole-residue pairs of the impedance functions, which can be calculated by fast and efficient recursive convolution. The numerical results agree very well with experi- mental data in the situations of weak nonlinear wave propagation in an exponential horn, it is shown that the model can describe the broadband characteristics caused by nonlinear distortion. Moreover, finite-amplitude acoustic propagation in types of horns is simulated, including hyperbolic, conical, exponential and sinusoidal horns. It is found that sound pressure levels at the horn mouth are strongly affected by the horn profiles, the driving velocity and frequency of the piston. The paper also discusses the influence of the horn geometry on nonlinear waveform distortion.展开更多
By using the method of dynamical system, the exact travelling wave solutions of the coupled nonlinear Schrdinger-KdV equations are studied. Based on this method, all phase portraits of the system in the parametric spa...By using the method of dynamical system, the exact travelling wave solutions of the coupled nonlinear Schrdinger-KdV equations are studied. Based on this method, all phase portraits of the system in the parametric space are given. All possible bounded travelling wave solutions such as solitary wave solutions and periodic travelling wave solutions are obtained. With the aid of Maple software, the numerical simulations are conducted for solitary wave solutions and periodic travelling wave solutions to the coupled nonlinear Schrdinger-KdV equations. The results show that the presented findings improve the related previous conclusions.展开更多
基金Supported by the Fund of National Nature Sciences of China
文摘This study deals with the general numerical model to simulate the two-dimensional tidal flow, flooding wave (long wave) and shallow water waves (short wave). The foundational model is based on nonlinear Boussinesq equations. Numerical method for modelling the short waves is investigated in detail. The forces, such as Coriolis forces, wind stress, atmosphere and bottom friction, are considered. A two-dimensional implicit difference scheme of Boussinesq equations is proposed. The low-reflection outflow open boundary is suggested. By means of this model,both velocity fields of circulation current in a channel with step expansion and the wave diffraction behind a semi-infinite breakwater are computed, and the results are satisfactory.
基金supported by the National Natural Science Foundation of China(51076005)
文摘Nonlinear acoustic propagation generated by a piston in a finite horn is numerically studied. A quasi-one-dimensional nonlinear model with varying cross-section uses high-order low-dispersion numerical schemes to solve the governing equation. Because of the nonlinear wave distortion and reflected sound waves at the mouth, broadband time-domain impedance boundary conditions are employed. The impedance approximation can be optimized to identify the complex-conjugate pole-residue pairs of the impedance functions, which can be calculated by fast and efficient recursive convolution. The numerical results agree very well with experi- mental data in the situations of weak nonlinear wave propagation in an exponential horn, it is shown that the model can describe the broadband characteristics caused by nonlinear distortion. Moreover, finite-amplitude acoustic propagation in types of horns is simulated, including hyperbolic, conical, exponential and sinusoidal horns. It is found that sound pressure levels at the horn mouth are strongly affected by the horn profiles, the driving velocity and frequency of the piston. The paper also discusses the influence of the horn geometry on nonlinear waveform distortion.
文摘By using the method of dynamical system, the exact travelling wave solutions of the coupled nonlinear Schrdinger-KdV equations are studied. Based on this method, all phase portraits of the system in the parametric space are given. All possible bounded travelling wave solutions such as solitary wave solutions and periodic travelling wave solutions are obtained. With the aid of Maple software, the numerical simulations are conducted for solitary wave solutions and periodic travelling wave solutions to the coupled nonlinear Schrdinger-KdV equations. The results show that the presented findings improve the related previous conclusions.
