To investigate the hydrodynamic characteristic of pontoon bridge, the multi-block grid generation technique with numerical methods for viscous fluid dynamics is applied to numerical simulations on the hydrodynamic cha...To investigate the hydrodynamic characteristic of pontoon bridge, the multi-block grid generation technique with numerical methods for viscous fluid dynamics is applied to numerical simulations on the hydrodynamic characteristic of a ribbon ferrying raft model at a series of towing speeds. Comparison of the simulated results with the experimental data indicates that the simulated results are acceptable. It shows that the multi-block grid generation technique is effective in the computation on pontoon bridge hydrodynamics.展开更多
This paper focuses on the development of a hybrid method with block extension for direct solution of initial value problems (IVPs) of general third-order ordinary differential equations. Power series was used as the b...This paper focuses on the development of a hybrid method with block extension for direct solution of initial value problems (IVPs) of general third-order ordinary differential equations. Power series was used as the basis function for the solution of the IVP. An approximate solution from the basis function was interpolated at some selected off-grid points while the third derivative of the approximate solution was collocated at all grid and off-grid points to generate a system of linear equations for the determination of the unknown parameters. The derived method was tested for consistency, zero stability, convergence and absolute stability. The method was implemented with five test problems including the Genesio equation to confirm its accuracy and usability. The rate of convergence (ROC) reveals that the method is consistent with the theoretical order of the proposed method. Comparison of the results with some existing methods shows the superiority of the accuracy of the method.展开更多
In this paper the algebraic multi-grid principle is applied to the multilevel moment method, which makes the new multilevel method easier to implement and more adaptive to structure. Moreover, the error spectrum is an...In this paper the algebraic multi-grid principle is applied to the multilevel moment method, which makes the new multilevel method easier to implement and more adaptive to structure. Moreover, the error spectrum is analyzed, and the reason why conjugate gradient iteration is not a good relaxation scheme for multi-grid algorithm is explored. The numerical results show that our algebraic block Gauss Seidel multi-grid algorithm is very effective.展开更多
Theory has it that increasing the step length improves the accuracy of a method. In order to affirm this we increased the step length of the concept in [1] by one to get k = 5. The technique of collocation and interpo...Theory has it that increasing the step length improves the accuracy of a method. In order to affirm this we increased the step length of the concept in [1] by one to get k = 5. The technique of collocation and interpolation of the power series approximate solution at some selected grid points is considered so as to generate continuous linear multistep methods with constant step sizes. Two, three and four interpolation points are considered to generate the continuous predictor-corrector methods which are implemented in block method respectively. The proposed methods when tested on some numerical examples performed more efficiently than those of [1]. Interestingly the concept of self starting [2] and that of constant order are reaffirmed in our new methods.展开更多
Beijing is a typical traditional city in China,originating from the uniform and conventional grid plan,but transformed diversely,either on purpose or spontaneously.This research took the diversification process of gri...Beijing is a typical traditional city in China,originating from the uniform and conventional grid plan,but transformed diversely,either on purpose or spontaneously.This research took the diversification process of grid blocks as an angle to understand the transformation process of Beijing’s urban morphology.It took 194 grid blocks within the 3rd Ring Road of Beijing as research objects.First,the paper proposed a whole view of Beijing’s grid blocks by 1)visualizing their construction process,2)classifying 5 morphological clusters by 7 indicators(Block size,Block shape regularity,Intensity,Coverage,Network density,Plot shape regularity,Standard deviation of plot size),and 3)investigating their distribution.Second,the diversification process of grid blocks was clarified from two layers:the block-boundary layer and the inner-space layer.Finally,the mechanism of block form diversification was clarified by exploring the connections between elements in each layer,and the influence of urban development on block form transformation.The study re-defined the diversification process in a more quantitative way from both time and spatial dimension.It concluded that the diversification is influenced by changes in urban planning principles and locations,and emerged thorough the long-term transformation and resubdivision.The interaction between the boundary and the inner space stimulates the diversification.And based on these,it concluded with a discussion of limitations and potentials on grid blocks’construction and renovation.展开更多
文摘To investigate the hydrodynamic characteristic of pontoon bridge, the multi-block grid generation technique with numerical methods for viscous fluid dynamics is applied to numerical simulations on the hydrodynamic characteristic of a ribbon ferrying raft model at a series of towing speeds. Comparison of the simulated results with the experimental data indicates that the simulated results are acceptable. It shows that the multi-block grid generation technique is effective in the computation on pontoon bridge hydrodynamics.
基金This work is supported in partial by Major State Basic Research Project （No. G19990328, Parallel Computations of the Large-Scale Reservoir Simulation （2003-2004） （Cooperated with China National 0ffshore 0il Corporation）, and National Natural Science Foundation Project （No. 60303020, 2004.1-2006.12）.
文摘This paper focuses on the development of a hybrid method with block extension for direct solution of initial value problems (IVPs) of general third-order ordinary differential equations. Power series was used as the basis function for the solution of the IVP. An approximate solution from the basis function was interpolated at some selected off-grid points while the third derivative of the approximate solution was collocated at all grid and off-grid points to generate a system of linear equations for the determination of the unknown parameters. The derived method was tested for consistency, zero stability, convergence and absolute stability. The method was implemented with five test problems including the Genesio equation to confirm its accuracy and usability. The rate of convergence (ROC) reveals that the method is consistent with the theoretical order of the proposed method. Comparison of the results with some existing methods shows the superiority of the accuracy of the method.
基金Supported by the Natlonal Natural Science Foundation of China
文摘In this paper the algebraic multi-grid principle is applied to the multilevel moment method, which makes the new multilevel method easier to implement and more adaptive to structure. Moreover, the error spectrum is analyzed, and the reason why conjugate gradient iteration is not a good relaxation scheme for multi-grid algorithm is explored. The numerical results show that our algebraic block Gauss Seidel multi-grid algorithm is very effective.
文摘Theory has it that increasing the step length improves the accuracy of a method. In order to affirm this we increased the step length of the concept in [1] by one to get k = 5. The technique of collocation and interpolation of the power series approximate solution at some selected grid points is considered so as to generate continuous linear multistep methods with constant step sizes. Two, three and four interpolation points are considered to generate the continuous predictor-corrector methods which are implemented in block method respectively. The proposed methods when tested on some numerical examples performed more efficiently than those of [1]. Interestingly the concept of self starting [2] and that of constant order are reaffirmed in our new methods.
基金funded by the National Natural Science Foundation of China(Grant Nos.52308030,52038007)Cultivation of Leading Innovative Talents in Science and Technology at Tianjin University“Qiming Plan”Program(Grant No.2023XQM-0044).
文摘Beijing is a typical traditional city in China,originating from the uniform and conventional grid plan,but transformed diversely,either on purpose or spontaneously.This research took the diversification process of grid blocks as an angle to understand the transformation process of Beijing’s urban morphology.It took 194 grid blocks within the 3rd Ring Road of Beijing as research objects.First,the paper proposed a whole view of Beijing’s grid blocks by 1)visualizing their construction process,2)classifying 5 morphological clusters by 7 indicators(Block size,Block shape regularity,Intensity,Coverage,Network density,Plot shape regularity,Standard deviation of plot size),and 3)investigating their distribution.Second,the diversification process of grid blocks was clarified from two layers:the block-boundary layer and the inner-space layer.Finally,the mechanism of block form diversification was clarified by exploring the connections between elements in each layer,and the influence of urban development on block form transformation.The study re-defined the diversification process in a more quantitative way from both time and spatial dimension.It concluded that the diversification is influenced by changes in urban planning principles and locations,and emerged thorough the long-term transformation and resubdivision.The interaction between the boundary and the inner space stimulates the diversification.And based on these,it concluded with a discussion of limitations and potentials on grid blocks’construction and renovation.
