In this paper, we propose a two-grid algorithm for solving the stream function formulation of the stationary Navies-Stokes equations. The algorithm is constructed by reducing the original system to one small, nonlinea...In this paper, we propose a two-grid algorithm for solving the stream function formulation of the stationary Navies-Stokes equations. The algorithm is constructed by reducing the original system to one small, nonlinear system on the coarse mesh space and two similar linear systems （with same stiffness matrix but different right-hand side） on the fine mesh space. The convergence analysis and error estimation of the algorithm are given for the case of conforming elements. Furthermore, the Mgorithm produces a numerical solution with the optimal asymptotic H^2-error. Finally, we give a numerical illustration to demonstrate the effectiveness of the two-grid algorithm for solving the Navier-Stokes equations.展开更多
Two-level finite element approximation to stream function form of unsteady Navier-Stokes equations is studied.This algorithm involves solving one nonlinear system on a coarse grid and one linear problem on a fine grid...Two-level finite element approximation to stream function form of unsteady Navier-Stokes equations is studied.This algorithm involves solving one nonlinear system on a coarse grid and one linear problem on a fine grid.Moreover,the scaling between these two grid sizes is super-linear.Approximation,stability and convergence aspects of a fully discrete scheme are analyzed.At last a numrical example is given whose results show that the algorithm proposed in this paper is effcient.展开更多
The stream function and the velocity potential can be easily computed by solving the Poisson equations in a unique way for the global domain. Because of the var- ious assumptions for handling the boundary conditions, ...The stream function and the velocity potential can be easily computed by solving the Poisson equations in a unique way for the global domain. Because of the var- ious assumptions for handling the boundary conditions, the solution is not unique when a limited domain is concerned. Therefore, it is very important to reduce or eliminate the effects caused by the uncertain boundary condition. In this paper, an iterative and ad- justing method based on the Endlich iteration method is presented to compute the stream function and the velocity potential in limited domains. This method does not need an explicitly specifying boundary condition when used to obtain the effective solution, and it is proved to be successful in decomposing and reconstructing the horizontal wind field with very small errors. The convergence of the method depends on the relative value for the distances of grids in two different directions and the value of the adjusting factor. It is shown that applying the method in Arakawa grids and irregular domains can obtain the accurate vorticity and divergence and accurately decompose and reconstruct the original wind field. Hence, the iterative and adjusting method is accurate and reliable.展开更多
Residual based on a posteriori error estimates for conforming finite element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level met...Residual based on a posteriori error estimates for conforming finite element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level method were derived. The posteriori error estimates contained additional terms in comparison to the error estimates for the solution obtained by the standard finite element method. The importance of these additional terms in the error estimates was investigated by studying their asymptotic behavior. For optimal scaled meshes, these bounds are not of higher order than of convergence of discrete solution.展开更多
Based on the linear wave, solitary wave and fifth order stokes wave derived by use of the Unified Variational Principle of Water Gravity Wave (UVPWGW), this paper derives stream function wave theory by using UVPWGW. T...Based on the linear wave, solitary wave and fifth order stokes wave derived by use of the Unified Variational Principle of Water Gravity Wave (UVPWGW), this paper derives stream function wave theory by using UVPWGW. This paper will handle the Kinematic Free Surface Boundary Condition (KFSBC) and Dynamic Free Surface Boundary Condition (DFSBC) directly and give the optimum solution, instead of the conditions Sigma(Q(av) - Q(i))(2) = min, and the related equations of stational condition. When the wave height H, period T and water depth D are given, the original stream function wave will be determined, and can not be adjusted if it does not agree with the real case; in the present method, the adjustment can be done by adding several constraint conditions, for example, the wave profile can be adjusted according to the condition of accurate peak position. The examples given in this paper show that for the original stream function wave, the DFSBC can be fairly well satisfied, but the KFSBC can not; however, the stream function wave derived by UVPWGW is better than the original one in the sense of minimum error squares in the aspect of the level at which KFSBC and DFSBC are satisfied.展开更多
Typical Hall plates for practical magnetic field sensing purposes are plane, simply-connected regions with peripheral contacts. Their output voltage is the sum of even and odd functions of the applied magnetic field. ...Typical Hall plates for practical magnetic field sensing purposes are plane, simply-connected regions with peripheral contacts. Their output voltage is the sum of even and odd functions of the applied magnetic field. They are commonly called offset and Hall voltage. Contemporary smart Hall sensor circuits extract the Hall voltage via spinning current Hall probe schemes, thereby cancelling out the offset very efficiently. The magnetic field response of such Hall plates can be computed via the electric potential or via the stream function. Conversely, Hall plates with holes show new phenomena: 1) the stream function exists only for a limited class of multiply-connected domains, and 2) a sub-class of 1) behaves like a Hall/Anti-Hall bar configuration, i.e., no Hall voltage appears between any two points on the hole boundary if current contacts are on their outer boundary. The paper studies the requirements under which these effects occur. Canonical cases of simply and doubly connected domains are computed analytically. The focus is on 2D multiply-connected Hall plates where all boundaries are insulating and where all current contacts are point sized.展开更多
The finite element solution of a generalized Stokes system in terms of the flow variables stream function and vorticity is studied. This system results from a time discretization of the time-dependent Stokes system in...The finite element solution of a generalized Stokes system in terms of the flow variables stream function and vorticity is studied. This system results from a time discretization of the time-dependent Stokes system in stream function-vorticity formulation, or yet by the application of the characteristics method to solve the Navier-Stokes equations in the same representation. Numerical results presented for both cases illustrate the good behaviour of the adopted approach.展开更多
A fine-grid model (1/6) covering the South China Sea (SCS), East China Sea and Ja-pan/East Sea, which is embedded into a coarse-grid (3) global model, was established to study the SCS circulation. In the present paper...A fine-grid model (1/6) covering the South China Sea (SCS), East China Sea and Ja-pan/East Sea, which is embedded into a coarse-grid (3) global model, was established to study the SCS circulation. In the present paper, we report the model-produced monthly and annual mean transport stream functions and sea surface heights(SSH) and their anomalies of the SCS. Com-parison to the TOPEX/Poseidon data shows that the model-produced monthly sea surface height anomalies (SSHA) are in good agreement with altimeter measurements. Based on the results, the circulation of the SCS, especially the upper layer circulation, is discussed. In the surface layer, the western Philippine Sea water intrudes into the SCS through the Luzon Strait in autumn, winter and spring, but not in summer. However, as far as the whole water column is concerned, the water in-trudes into the SCS through the Luzon Strait all the year round. This indicates that in summer the water still intrudes into the SCS in the subsurface and intermediate layers. The area near the northern continental slope of the SCS is dominated by a cyclonic circulation all the year round. The SCS Southern Anticyclonic Gyre, SE Vietnam Off-Shore Current in summertime and SCS South-ern Cyclonic Gyre in wintertime are reproduced reasonably. The difference between the monthly averaged SSH and SSHA is significant, indicating the importance of the mean SSH in the SCS circulation.展开更多
The artificial density method which has been applied widely in the transonic potential calculation and the current transonic stream function calculation is investigated theoretically. The analysis shows that in the st...The artificial density method which has been applied widely in the transonic potential calculation and the current transonic stream function calculation is investigated theoretically. The analysis shows that in the stream function formulation the artificial density is not equivalent to the artificial viscosity and cannot be used, and a correct expression of the artificial viscosity in the stream function method is then derived. The principal equation of the stream function, the density equation converted from one of the momentum equations and the present artificial viscosity scheme constitute the complete transonic stream function formulation. The numerical practice demonstrates that the range of Mach number computed by this approach is extended and the shock location is close to the experimental result.展开更多
Several kinds of stream ciphers—complementary sequences of period sequences,partial sum of period sequences,inverse order sequences and finitely generated sequences,arestudied by using techniques of generating functi...Several kinds of stream ciphers—complementary sequences of period sequences,partial sum of period sequences,inverse order sequences and finitely generated sequences,arestudied by using techniques of generating functions.Their minimal polynomials,periods,as wellas generating functions are given.As to finitely generated sequences,the change of their linearcomplexity profiles as well as the relationship between the two generated sequences usder thecase in which the degree of connected polynomials are fixed,are discussed.展开更多
The nonlinear filter Boolean function of LILI-128 stream cipher generator is studied in this paper. First we measure the complexity of the stream ciphers sequence of LILI-128 stream cipher generator and obtain the sho...The nonlinear filter Boolean function of LILI-128 stream cipher generator is studied in this paper. First we measure the complexity of the stream ciphers sequence of LILI-128 stream cipher generator and obtain the shortest bit stream sequence reconstructed Boolean function of nonlinear filter in LILI-128 stream cipher generator. Then the least nonlinear Boolean function of generating stream cipher sequence is reconstructed by clusterig, nonlinear predictive and nonlinear synchronization from shortest bit stream sequence. We have verified the correctness of our reconstruction result by simulating the block diagram of Lili-128 keystream generator using our getting Boolean function and implement designers’ reference module of Lili-128 stream cipher public online, and two methods produce the same synchronous keystream sequence under same initial state, so that our research work proves that the nonlinear Boolean function of LILI-128 stream cipher generator is successfully broken.展开更多
A heavy rainfall event that occurred over the middle and lower reaches of the Yangtze River Basin （YRB） during July 11-13 2000 is explored in this study. The potential/stream function is used to analyze the upstream...A heavy rainfall event that occurred over the middle and lower reaches of the Yangtze River Basin （YRB） during July 11-13 2000 is explored in this study. The potential/stream function is used to analyze the upstream ＂strong signals＂ of the water vapor transport in the Tibetan Plateau （TP）. The studied time period covers from 2000 LST 5 July to 2000 LST 15 July （temporal resolution： 6 hours）. By analyzing the three-dimensional structure of the water vapor flux, vorticity and divergence prior to and during the heavy rainfall event, the upstream ＂strong signals＂ related to this heavy rainfall event are revealed. A strong correlation exists between the heavy rainfall event in the YRB and the convective clouds over the TE The ＂convergence zone＂ of the water vapor transport is also identified, based on correlation analysis of the water vapor flux two days and one day prior to, and on the day of, the heavy rainfall. And this ＂convergence zone＂ coincides with the migration of the maximum rainfall over the YRB. This specific coupled structure actually plays a key role in generating heavy rainfall over the YRB. The eastward movement of the coupled system with a divergence]convergence center of the potential function at the upper/lower level resembles the spatiotemporal evolution of the heavy rainfall event over the YRB. These upstream ＂strong signals＂ are clearly traced in this study through analyzing the three-dimensional structure of the potential/stream function of upstream water vapor transport.展开更多
A nonlinear Galerkin finite element method is presented for the two dimensional incom- pressible Navier-Stokes equations with stream-vorticity form.the scheme is based on two finite ele- ment spaces XH and XH for the ...A nonlinear Galerkin finite element method is presented for the two dimensional incom- pressible Navier-Stokes equations with stream-vorticity form.the scheme is based on two finite ele- ment spaces XH and XH for the approximation of the stream and vorticity function ,defined respec- tively on a coarse grid with grid size H and a fine grid with grid size h<<H.We prove that the difference between the new nonlinear Galerkin method and the standard Galerkin method is of the order H2both in stream function and vorticity.展开更多
A large class of linear structural functions(LSF) satisfying the condition of correlational immunity of order one are constructed by studying the linear structural Boolean functions. With these new founded functions, ...A large class of linear structural functions(LSF) satisfying the condition of correlational immunity of order one are constructed by studying the linear structural Boolean functions. With these new founded functions, the known enumeration bounds of correlation-immune functions of order one are greatly improved. In fact, the best, up to now, lower bound is found.展开更多
基金supported by National Foundation of Natural Science under the Grant 11071216
文摘In this paper, we propose a two-grid algorithm for solving the stream function formulation of the stationary Navies-Stokes equations. The algorithm is constructed by reducing the original system to one small, nonlinear system on the coarse mesh space and two similar linear systems （with same stiffness matrix but different right-hand side） on the fine mesh space. The convergence analysis and error estimation of the algorithm are given for the case of conforming elements. Furthermore, the Mgorithm produces a numerical solution with the optimal asymptotic H^2-error. Finally, we give a numerical illustration to demonstrate the effectiveness of the two-grid algorithm for solving the Navier-Stokes equations.
文摘Two-level finite element approximation to stream function form of unsteady Navier-Stokes equations is studied.This algorithm involves solving one nonlinear system on a coarse grid and one linear problem on a fine grid.Moreover,the scaling between these two grid sizes is super-linear.Approximation,stability and convergence aspects of a fully discrete scheme are analyzed.At last a numrical example is given whose results show that the algorithm proposed in this paper is effcient.
基金Project supported by the National Natural Science Foundation of China (No.40975031)
文摘The stream function and the velocity potential can be easily computed by solving the Poisson equations in a unique way for the global domain. Because of the var- ious assumptions for handling the boundary conditions, the solution is not unique when a limited domain is concerned. Therefore, it is very important to reduce or eliminate the effects caused by the uncertain boundary condition. In this paper, an iterative and ad- justing method based on the Endlich iteration method is presented to compute the stream function and the velocity potential in limited domains. This method does not need an explicitly specifying boundary condition when used to obtain the effective solution, and it is proved to be successful in decomposing and reconstructing the horizontal wind field with very small errors. The convergence of the method depends on the relative value for the distances of grids in two different directions and the value of the adjusting factor. It is shown that applying the method in Arakawa grids and irregular domains can obtain the accurate vorticity and divergence and accurately decompose and reconstruct the original wind field. Hence, the iterative and adjusting method is accurate and reliable.
文摘Residual based on a posteriori error estimates for conforming finite element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level method were derived. The posteriori error estimates contained additional terms in comparison to the error estimates for the solution obtained by the standard finite element method. The importance of these additional terms in the error estimates was investigated by studying their asymptotic behavior. For optimal scaled meshes, these bounds are not of higher order than of convergence of discrete solution.
文摘Based on the linear wave, solitary wave and fifth order stokes wave derived by use of the Unified Variational Principle of Water Gravity Wave (UVPWGW), this paper derives stream function wave theory by using UVPWGW. This paper will handle the Kinematic Free Surface Boundary Condition (KFSBC) and Dynamic Free Surface Boundary Condition (DFSBC) directly and give the optimum solution, instead of the conditions Sigma(Q(av) - Q(i))(2) = min, and the related equations of stational condition. When the wave height H, period T and water depth D are given, the original stream function wave will be determined, and can not be adjusted if it does not agree with the real case; in the present method, the adjustment can be done by adding several constraint conditions, for example, the wave profile can be adjusted according to the condition of accurate peak position. The examples given in this paper show that for the original stream function wave, the DFSBC can be fairly well satisfied, but the KFSBC can not; however, the stream function wave derived by UVPWGW is better than the original one in the sense of minimum error squares in the aspect of the level at which KFSBC and DFSBC are satisfied.
文摘Typical Hall plates for practical magnetic field sensing purposes are plane, simply-connected regions with peripheral contacts. Their output voltage is the sum of even and odd functions of the applied magnetic field. They are commonly called offset and Hall voltage. Contemporary smart Hall sensor circuits extract the Hall voltage via spinning current Hall probe schemes, thereby cancelling out the offset very efficiently. The magnetic field response of such Hall plates can be computed via the electric potential or via the stream function. Conversely, Hall plates with holes show new phenomena: 1) the stream function exists only for a limited class of multiply-connected domains, and 2) a sub-class of 1) behaves like a Hall/Anti-Hall bar configuration, i.e., no Hall voltage appears between any two points on the hole boundary if current contacts are on their outer boundary. The paper studies the requirements under which these effects occur. Canonical cases of simply and doubly connected domains are computed analytically. The focus is on 2D multiply-connected Hall plates where all boundaries are insulating and where all current contacts are point sized.
文摘The finite element solution of a generalized Stokes system in terms of the flow variables stream function and vorticity is studied. This system results from a time discretization of the time-dependent Stokes system in stream function-vorticity formulation, or yet by the application of the characteristics method to solve the Navier-Stokes equations in the same representation. Numerical results presented for both cases illustrate the good behaviour of the adopted approach.
基金the China Major State Basic Research Program (Grant No. G1999043808) the Youth Fund of National 863 Project (Grant No. 2002AA639350) the National Natural Science Foundation of China (Grant No. 49876010) and the Innovation Program of the Chinese Aca
文摘A fine-grid model (1/6) covering the South China Sea (SCS), East China Sea and Ja-pan/East Sea, which is embedded into a coarse-grid (3) global model, was established to study the SCS circulation. In the present paper, we report the model-produced monthly and annual mean transport stream functions and sea surface heights(SSH) and their anomalies of the SCS. Com-parison to the TOPEX/Poseidon data shows that the model-produced monthly sea surface height anomalies (SSHA) are in good agreement with altimeter measurements. Based on the results, the circulation of the SCS, especially the upper layer circulation, is discussed. In the surface layer, the western Philippine Sea water intrudes into the SCS through the Luzon Strait in autumn, winter and spring, but not in summer. However, as far as the whole water column is concerned, the water in-trudes into the SCS through the Luzon Strait all the year round. This indicates that in summer the water still intrudes into the SCS in the subsurface and intermediate layers. The area near the northern continental slope of the SCS is dominated by a cyclonic circulation all the year round. The SCS Southern Anticyclonic Gyre, SE Vietnam Off-Shore Current in summertime and SCS South-ern Cyclonic Gyre in wintertime are reproduced reasonably. The difference between the monthly averaged SSH and SSHA is significant, indicating the importance of the mean SSH in the SCS circulation.
文摘The artificial density method which has been applied widely in the transonic potential calculation and the current transonic stream function calculation is investigated theoretically. The analysis shows that in the stream function formulation the artificial density is not equivalent to the artificial viscosity and cannot be used, and a correct expression of the artificial viscosity in the stream function method is then derived. The principal equation of the stream function, the density equation converted from one of the momentum equations and the present artificial viscosity scheme constitute the complete transonic stream function formulation. The numerical practice demonstrates that the range of Mach number computed by this approach is extended and the shock location is close to the experimental result.
文摘Several kinds of stream ciphers—complementary sequences of period sequences,partial sum of period sequences,inverse order sequences and finitely generated sequences,arestudied by using techniques of generating functions.Their minimal polynomials,periods,as wellas generating functions are given.As to finitely generated sequences,the change of their linearcomplexity profiles as well as the relationship between the two generated sequences usder thecase in which the degree of connected polynomials are fixed,are discussed.
文摘The nonlinear filter Boolean function of LILI-128 stream cipher generator is studied in this paper. First we measure the complexity of the stream ciphers sequence of LILI-128 stream cipher generator and obtain the shortest bit stream sequence reconstructed Boolean function of nonlinear filter in LILI-128 stream cipher generator. Then the least nonlinear Boolean function of generating stream cipher sequence is reconstructed by clusterig, nonlinear predictive and nonlinear synchronization from shortest bit stream sequence. We have verified the correctness of our reconstruction result by simulating the block diagram of Lili-128 keystream generator using our getting Boolean function and implement designers’ reference module of Lili-128 stream cipher public online, and two methods produce the same synchronous keystream sequence under same initial state, so that our research work proves that the nonlinear Boolean function of LILI-128 stream cipher generator is successfully broken.
文摘A heavy rainfall event that occurred over the middle and lower reaches of the Yangtze River Basin （YRB） during July 11-13 2000 is explored in this study. The potential/stream function is used to analyze the upstream ＂strong signals＂ of the water vapor transport in the Tibetan Plateau （TP）. The studied time period covers from 2000 LST 5 July to 2000 LST 15 July （temporal resolution： 6 hours）. By analyzing the three-dimensional structure of the water vapor flux, vorticity and divergence prior to and during the heavy rainfall event, the upstream ＂strong signals＂ related to this heavy rainfall event are revealed. A strong correlation exists between the heavy rainfall event in the YRB and the convective clouds over the TE The ＂convergence zone＂ of the water vapor transport is also identified, based on correlation analysis of the water vapor flux two days and one day prior to, and on the day of, the heavy rainfall. And this ＂convergence zone＂ coincides with the migration of the maximum rainfall over the YRB. This specific coupled structure actually plays a key role in generating heavy rainfall over the YRB. The eastward movement of the coupled system with a divergence]convergence center of the potential function at the upper/lower level resembles the spatiotemporal evolution of the heavy rainfall event over the YRB. These upstream ＂strong signals＂ are clearly traced in this study through analyzing the three-dimensional structure of the potential/stream function of upstream water vapor transport.
文摘A nonlinear Galerkin finite element method is presented for the two dimensional incom- pressible Navier-Stokes equations with stream-vorticity form.the scheme is based on two finite ele- ment spaces XH and XH for the approximation of the stream and vorticity function ,defined respec- tively on a coarse grid with grid size H and a fine grid with grid size h<<H.We prove that the difference between the new nonlinear Galerkin method and the standard Galerkin method is of the order H2both in stream function and vorticity.
文摘A large class of linear structural functions(LSF) satisfying the condition of correlational immunity of order one are constructed by studying the linear structural Boolean functions. With these new founded functions, the known enumeration bounds of correlation-immune functions of order one are greatly improved. In fact, the best, up to now, lower bound is found.
