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
A reverberation model for estimating the average reverberation intensity in layered shallow water is presented.The reverberation intensity is calculated in terms of ray theory for short range and normal mode theory fo...A reverberation model for estimating the average reverberation intensity in layered shallow water is presented.The reverberation intensity is calculated in terms of ray theory for short range and normal mode theory for long range. The calculation accuracy has been improved by taking into account the effect of complex eigenvalues on the incident normal mode field. From the comparison between different scattering models it has been shown that the separable bistatic-backscattering model is acceptable. This makes it possible to calculate reverberation by using only the monostatic-backscattering coefficient and to save greatly the computing time.展开更多
This paper continues discussing the problems of numerically solving the shallow water circulation on the basis of ref. 1, For the numerical method proposed in ref. 1, we applied a storage method with dense matrices, w...This paper continues discussing the problems of numerically solving the shallow water circulation on the basis of ref. 1, For the numerical method proposed in ref. 1, we applied a storage method with dense matrices, which abandoned usual bandwidth concept and attained the intention of saving interior storage, computing time and amount of preparing work before computing. The circulation considered the effect of small islands was successfully simulated by specially dealing with the bottom friction terms and the boundary conditions. In addition, we discussed the action of bottom friction on the dissipation of tidal energy and its effect on stability of period motion.展开更多
Imbalance arises when the Roe＇s method is directly applied in the shallow water simulation.The reasons are different for the continuity equation and the momentum equations.Based on the Roe＇s method,a partial surface...Imbalance arises when the Roe＇s method is directly applied in the shallow water simulation.The reasons are different for the continuity equation and the momentum equations.Based on the Roe＇s method,a partial surface method is proposed for a perfect balance for the continuity equation.In order to generate a mathematically hyperbolic formulation,the momentum equations are split,which causes incompatibility in the calculation of the momentum equations.In this article a numerical approach named the Slop Flux Method（SFM）is proposed to balance the source terms and the flux gradient based on the finite volume method.The method is first applied to shallow water equations.The model is verified by analytical results of classical test cases with good agreement.Finally the method is applied to a steady flow simulation over a practical complicated topography and the result shows good balance and conservation.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.
文摘A reverberation model for estimating the average reverberation intensity in layered shallow water is presented.The reverberation intensity is calculated in terms of ray theory for short range and normal mode theory for long range. The calculation accuracy has been improved by taking into account the effect of complex eigenvalues on the incident normal mode field. From the comparison between different scattering models it has been shown that the separable bistatic-backscattering model is acceptable. This makes it possible to calculate reverberation by using only the monostatic-backscattering coefficient and to save greatly the computing time.
文摘This paper continues discussing the problems of numerically solving the shallow water circulation on the basis of ref. 1, For the numerical method proposed in ref. 1, we applied a storage method with dense matrices, which abandoned usual bandwidth concept and attained the intention of saving interior storage, computing time and amount of preparing work before computing. The circulation considered the effect of small islands was successfully simulated by specially dealing with the bottom friction terms and the boundary conditions. In addition, we discussed the action of bottom friction on the dissipation of tidal energy and its effect on stability of period motion.
基金supported by the National Basic Research and Development Program of China(973Program,Grant No.2011CB409901)the Special Funds for Public Welfare Project(Grant No.200901014)the"12th Five-Year Plan"to Support Science and Technology Project(Grant No.2012BAB02B01)
文摘Imbalance arises when the Roe＇s method is directly applied in the shallow water simulation.The reasons are different for the continuity equation and the momentum equations.Based on the Roe＇s method,a partial surface method is proposed for a perfect balance for the continuity equation.In order to generate a mathematically hyperbolic formulation,the momentum equations are split,which causes incompatibility in the calculation of the momentum equations.In this article a numerical approach named the Slop Flux Method（SFM）is proposed to balance the source terms and the flux gradient based on the finite volume method.The method is first applied to shallow water equations.The model is verified by analytical results of classical test cases with good agreement.Finally the method is applied to a steady flow simulation over a practical complicated topography and the result shows good balance and conservation.
