This paper presents a numerical model study of the propagation of water waves using the parabolic approximation of the mild slope equation in the orthogonal coordinate system. Two types of coordinate systems are stud...This paper presents a numerical model study of the propagation of water waves using the parabolic approximation of the mild slope equation in the orthogonal coordinate system. Two types of coordinate systems are studied: (a) a general form of orthogonal coordinate system and (b) the conformal system, a special form of orthogonal coordinate system. Two typical examples, namely, expanded breakwaters and a circular channel, are studied to validate the model. First, the examples are studied by use of the general orthogonal coordinates. Then the same examples are computed by use of the conformal system. The computational results show that the conformal coordinate system generally gives better predictions than the general orthogonal system. A numerical technique for generating the conformal grid is combined with the numerical model to improve the practicability of the model. The comparison between the result from the numerical grid system and that from the analytical grid system shows that reliable computational results can be obtained by use of the numerical conformal grid system.展开更多
The velocity field in meandering compound channels with overhank flow is highly three dimensional. To date, its features have been investigated experimentally and little research has been undertaken to investigate the...The velocity field in meandering compound channels with overhank flow is highly three dimensional. To date, its features have been investigated experimentally and little research has been undertaken to investigate the feasibility of reproducing these velocity fields with computer models. If computer modeling were to prove successful in this context, it could become a useful prediction technique and research tool to enhance our understanding of natural river dynamics. A 3-D k-E turbulence hydrodynamic model in curvilinear coordinates is established to simulate the overhank flow. The bodyfitted coordinate is adopted in the horizontal plane, the part grid is adopted in the vertical direction, and the wall-function method is employed to simulate the bed resistance. The model is applied to the simulation of the meandering channel with straight flood plain banks, and the main velocities and secondary velocities for both the longitudinal and cross sections are presented. Comparison and analysis show that the results of simulation are fit to reflect the results of experiment. These results show the application value of the model to 3D overhank flow.展开更多
It is explored that the line integral is a path independent in two or three arbitrary dimensional orthogonal curvilinear coordinate systems, which is based on the integral condition with the path independent in two or...It is explored that the line integral is a path independent in two or three arbitrary dimensional orthogonal curvilinear coordinate systems, which is based on the integral condition with the path independent in two or three dimensional rectangular coordinate systems. Firstly, according to the coordinate transformation, the condition that the line integral is the path independent in the polar coordinate system is obtained easily from the Green's theorem in two-dimensional rectangular coordinate system and the condition is extended to arbitrary two-dimension orthogonal curvilinear coordinates. Secondly, through the coordinate transformation relationship and the area projection method, the Stokes formula in three-dimensional rectangular coordinate system is promoted to the spherical coordinate system and cylindrical coordinate system, and the condition that the line integral is a path independent is obtained. Furthermore, the condition is extended to arbitrary three-dimension orthogonal curvilinear coordinates. Lastly, the conclusions are made.展开更多
Based on an analysis of connotation and extension of the concept of the orthogonal curvilinear coordinates, we have deduced a platform of strain tensor expression of Cartesian coordinates, which turns out to be a func...Based on an analysis of connotation and extension of the concept of the orthogonal curvilinear coordinates, we have deduced a platform of strain tensor expression of Cartesian coordinates, which turns out to be a function of Lame coefficient and unit vector. By using transform matrix between Cartesian coordinates and orthogonal eurvilinear coordinates, we have deduced a mathematical expression for correcting displacement vector differential in orthogonal curvilinear coordinates, and given a general expression of strain tensor in orthogonal curvilinear coordinates.展开更多
For shallow water flow, the depth-averaged governing equations are derived by depth-averaging of the mean equations for three-dimensional turbulent flows. The influences of free water surface and of topography of rive...For shallow water flow, the depth-averaged governing equations are derived by depth-averaging of the mean equations for three-dimensional turbulent flows. The influences of free water surface and of topography of river bed are taken into account.The depth-averaged equations of k-εturbulence model are also obtained. Because it Accounts for the three-dimensional effect, this model is named as the complete Depth-averaged model.The boundaries of natural water bodies are usually curved.In this work, the derived equations in Cartesian coordinates are transformed into orthogonal coordinates. The obtained equations can be applied directly to numerical computation of practical problems.展开更多
In this paper, the equilibrium equations on orthogonal curve coordinates made of curves of principal stresses are disscused and their properties in process of solution are presented through a simple example. Therefore...In this paper, the equilibrium equations on orthogonal curve coordinates made of curves of principal stresses are disscused and their properties in process of solution are presented through a simple example. Therefore, it is deduced that there is another way to solve problems in elasticity, i.e., by assumption of orthogonal curves of principal stresses.展开更多
In this paper, we got the best linear unbiased predictor of any linear function of the elements of a finite population under coordinate-free models. The optimal predictor of these quantities was obtained in an earlier...In this paper, we got the best linear unbiased predictor of any linear function of the elements of a finite population under coordinate-free models. The optimal predictor of these quantities was obtained in an earlier work considering models with a known diagonal covariance matrix. We extended this result assuming any known covariance matrix. It is shown that in the particular case of the coordinatized models, this general predictor coincides with the optimal predictor of the total population under a regression super population model with correlated observations.展开更多
A 2-D non-uniform sediment mat hmatical model in the boundary-fitting orthogonal coordinate system was develop ed in this paper. The governing equations, the numerical scheme, the boundary con ditions, the movable bou...A 2-D non-uniform sediment mat hmatical model in the boundary-fitting orthogonal coordinate system was develop ed in this paper. The governing equations, the numerical scheme, the boundary con ditions, the movable boundary technique and the numerical solutions were present ed. The model was verified by the data of the reach 25km upstream the Jialingjia ng estuary and the 44km long main stream of the Chongqing reach of the Yangtze r iver. The calculated results show that, the water elevation, the velocity distri bution and the river bed deformation are in agreement with the measured data.展开更多
This paper presents a numerical method for simulating the 2-D tidal flow andwater quality with the orthogonal curvilinear coordinates. In order to overcome the computationaldifficulties in natural rivers, such as the ...This paper presents a numerical method for simulating the 2-D tidal flow andwater quality with the orthogonal curvilinear coordinates. In order to overcome the computationaldifficulties in natural rivers, such as the complicated boundary figures, the great disparitybetween length and width of computational domain, etc. , orthogonal boundary-filled grid was used.The irregular domain in physical plane was transformed into a rectangular domain in a transformedplane, and the depth-averaged momentum equations and mass equation were given and discretized basedon the alternating direction implicit finite difference scheme in curvilinear coordinates. Theapplication of the presented method was illustrated by an example of analyzing the Yangtze River inthe vicinity of Nanjing city. A fair agreement between the measured data and computed resultsdemonstrates the validity of the developed method.展开更多
Channel assignment has emerged as an essential study subject in Cognitive Radio-basedWireless Mesh Networks(CR-WMN).In an era of alarming increase in Multi-Radio Multi-Channel(MRMC)network expansion interference is de...Channel assignment has emerged as an essential study subject in Cognitive Radio-basedWireless Mesh Networks(CR-WMN).In an era of alarming increase in Multi-Radio Multi-Channel(MRMC)network expansion interference is decreased and network throughput is significantly increased when non-overlapping or partially overlapping channels are correctly integrated.Because of its ad hoc behavior,dynamic channel assignment outperforms static channel assignment.Interference reduces network throughput in the CR-WMN.As a result,there is an extensive research gap for an algorithm that dynamically distributes channels while accounting for all types of interference.This work presents a method for dynamic channel allocations using unsupervisedMachine Learning(ML)that considers both coordinated and uncoordinated interference.Unsupervised machine learning uses coordinated and non-coordinated interference for dynamic channel allocation.To determine the applicability of the proposed strategy in reducing channel interference while increasingWMNthroughput,a comparison analysis was performed.When the simulation results of our proposed algorithm are compared to those of the Routing Channel Assignment(RCA)algorithm,the throughput of our proposed algorithm has increased by 34%compared to both coordinated and non-coordinated interferences.展开更多
文摘This paper presents a numerical model study of the propagation of water waves using the parabolic approximation of the mild slope equation in the orthogonal coordinate system. Two types of coordinate systems are studied: (a) a general form of orthogonal coordinate system and (b) the conformal system, a special form of orthogonal coordinate system. Two typical examples, namely, expanded breakwaters and a circular channel, are studied to validate the model. First, the examples are studied by use of the general orthogonal coordinates. Then the same examples are computed by use of the conformal system. The computational results show that the conformal coordinate system generally gives better predictions than the general orthogonal system. A numerical technique for generating the conformal grid is combined with the numerical model to improve the practicability of the model. The comparison between the result from the numerical grid system and that from the analytical grid system shows that reliable computational results can be obtained by use of the numerical conformal grid system.
文摘The velocity field in meandering compound channels with overhank flow is highly three dimensional. To date, its features have been investigated experimentally and little research has been undertaken to investigate the feasibility of reproducing these velocity fields with computer models. If computer modeling were to prove successful in this context, it could become a useful prediction technique and research tool to enhance our understanding of natural river dynamics. A 3-D k-E turbulence hydrodynamic model in curvilinear coordinates is established to simulate the overhank flow. The bodyfitted coordinate is adopted in the horizontal plane, the part grid is adopted in the vertical direction, and the wall-function method is employed to simulate the bed resistance. The model is applied to the simulation of the meandering channel with straight flood plain banks, and the main velocities and secondary velocities for both the longitudinal and cross sections are presented. Comparison and analysis show that the results of simulation are fit to reflect the results of experiment. These results show the application value of the model to 3D overhank flow.
基金Funded by the Natural Science Foundation Project of CQCSTC(No.cstc2012jj A50018)the Basic Research of Chongqing Municipal Education Commission(No.KJ120631)the Science Research Foundation Project of CQNU(No.16XYY31)
文摘It is explored that the line integral is a path independent in two or three arbitrary dimensional orthogonal curvilinear coordinate systems, which is based on the integral condition with the path independent in two or three dimensional rectangular coordinate systems. Firstly, according to the coordinate transformation, the condition that the line integral is the path independent in the polar coordinate system is obtained easily from the Green's theorem in two-dimensional rectangular coordinate system and the condition is extended to arbitrary two-dimension orthogonal curvilinear coordinates. Secondly, through the coordinate transformation relationship and the area projection method, the Stokes formula in three-dimensional rectangular coordinate system is promoted to the spherical coordinate system and cylindrical coordinate system, and the condition that the line integral is a path independent is obtained. Furthermore, the condition is extended to arbitrary three-dimension orthogonal curvilinear coordinates. Lastly, the conclusions are made.
文摘Based on an analysis of connotation and extension of the concept of the orthogonal curvilinear coordinates, we have deduced a platform of strain tensor expression of Cartesian coordinates, which turns out to be a function of Lame coefficient and unit vector. By using transform matrix between Cartesian coordinates and orthogonal eurvilinear coordinates, we have deduced a mathematical expression for correcting displacement vector differential in orthogonal curvilinear coordinates, and given a general expression of strain tensor in orthogonal curvilinear coordinates.
文摘For shallow water flow, the depth-averaged governing equations are derived by depth-averaging of the mean equations for three-dimensional turbulent flows. The influences of free water surface and of topography of river bed are taken into account.The depth-averaged equations of k-εturbulence model are also obtained. Because it Accounts for the three-dimensional effect, this model is named as the complete Depth-averaged model.The boundaries of natural water bodies are usually curved.In this work, the derived equations in Cartesian coordinates are transformed into orthogonal coordinates. The obtained equations can be applied directly to numerical computation of practical problems.
文摘In this paper, the equilibrium equations on orthogonal curve coordinates made of curves of principal stresses are disscused and their properties in process of solution are presented through a simple example. Therefore, it is deduced that there is another way to solve problems in elasticity, i.e., by assumption of orthogonal curves of principal stresses.
文摘In this paper, we got the best linear unbiased predictor of any linear function of the elements of a finite population under coordinate-free models. The optimal predictor of these quantities was obtained in an earlier work considering models with a known diagonal covariance matrix. We extended this result assuming any known covariance matrix. It is shown that in the particular case of the coordinatized models, this general predictor coincides with the optimal predictor of the total population under a regression super population model with correlated observations.
文摘A 2-D non-uniform sediment mat hmatical model in the boundary-fitting orthogonal coordinate system was develop ed in this paper. The governing equations, the numerical scheme, the boundary con ditions, the movable boundary technique and the numerical solutions were present ed. The model was verified by the data of the reach 25km upstream the Jialingjia ng estuary and the 44km long main stream of the Chongqing reach of the Yangtze r iver. The calculated results show that, the water elevation, the velocity distri bution and the river bed deformation are in agreement with the measured data.
文摘This paper presents a numerical method for simulating the 2-D tidal flow andwater quality with the orthogonal curvilinear coordinates. In order to overcome the computationaldifficulties in natural rivers, such as the complicated boundary figures, the great disparitybetween length and width of computational domain, etc. , orthogonal boundary-filled grid was used.The irregular domain in physical plane was transformed into a rectangular domain in a transformedplane, and the depth-averaged momentum equations and mass equation were given and discretized basedon the alternating direction implicit finite difference scheme in curvilinear coordinates. Theapplication of the presented method was illustrated by an example of analyzing the Yangtze River inthe vicinity of Nanjing city. A fair agreement between the measured data and computed resultsdemonstrates the validity of the developed method.
基金funded by the National Natural Science Foundation of China(61971014),Zhang Jianbiao.
文摘Channel assignment has emerged as an essential study subject in Cognitive Radio-basedWireless Mesh Networks(CR-WMN).In an era of alarming increase in Multi-Radio Multi-Channel(MRMC)network expansion interference is decreased and network throughput is significantly increased when non-overlapping or partially overlapping channels are correctly integrated.Because of its ad hoc behavior,dynamic channel assignment outperforms static channel assignment.Interference reduces network throughput in the CR-WMN.As a result,there is an extensive research gap for an algorithm that dynamically distributes channels while accounting for all types of interference.This work presents a method for dynamic channel allocations using unsupervisedMachine Learning(ML)that considers both coordinated and uncoordinated interference.Unsupervised machine learning uses coordinated and non-coordinated interference for dynamic channel allocation.To determine the applicability of the proposed strategy in reducing channel interference while increasingWMNthroughput,a comparison analysis was performed.When the simulation results of our proposed algorithm are compared to those of the Routing Channel Assignment(RCA)algorithm,the throughput of our proposed algorithm has increased by 34%compared to both coordinated and non-coordinated interferences.
