A vorticity-velocity method was used to study the incompressible viscous fluid flow around a circular cylinder with surface suction or blowing. The resulted high order implicit difference equations were effeciently so...A vorticity-velocity method was used to study the incompressible viscous fluid flow around a circular cylinder with surface suction or blowing. The resulted high order implicit difference equations were effeciently solved by the modified incomplete LU decomposition conjugate gradient scheme ( MILU-CG). The effects of surface suction or blowing' s position and strength on the vortex structures in the cylinder wake, as well as on the drag and lift forces at Reynoldes number Re = 100 were investigated numerically. The results show that the suction on the shoulder of the cylinder or the blowing on the rear of the cylinder can effeciently suppress the asymmetry of the vortex wake in the transverse direction and greatly reduce the lift force; the suction on the shoulder of the cylinder, when its strength is properly chosen, can reduce the drag force significantly, too.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
We investigate the ground states of spin-orbit coupled spin-1 Bose-Einstein condensates in the presence of Zeeman splitting.By introducing the generalized momentum operator,the linear version of the system is solved e...We investigate the ground states of spin-orbit coupled spin-1 Bose-Einstein condensates in the presence of Zeeman splitting.By introducing the generalized momentum operator,the linear version of the system is solved exactly,yielding a set of Bessel vortices.Additionally,based on linear solution and using variational approximation,the solutions for the full nonlinear system and their ground state phase diagrams are derived,including the vortex states with quantum numbers m=0,1,as well as mixed states.In this work,mixed states in spin-1 spin-orbit coupling(SOC)BEC are interpreted for the first time as weighted superpositions of three vortex states.Furthermore,the results also indicate that under strong Zeeman splitting,the system cannot form localized states.The variational solutions align well with numerical simulations,showing stable evolution and meeting the criteria for long-term observation in experiments.展开更多
The purpose of this article is to develop and analyze least-squares approximations for the incompressible magnetohydrodynamic equations. The major advantage of the least-squares finite element method is that it is not...The purpose of this article is to develop and analyze least-squares approximations for the incompressible magnetohydrodynamic equations. The major advantage of the least-squares finite element method is that it is not subjected to the so-called Ladyzhenskaya-Babuska-Brezzi （LBB） condition. The authors employ least-squares functionals which involve a discrete inner product which is related to the inner product in H^-1（Ω）.展开更多
The evolution of the three-dimensional time-developing mixing layer was simulated numerically using the pseudo-spectral method. The initial perturbations consisted of the two-dimensional fundamental wave and the stre...The evolution of the three-dimensional time-developing mixing layer was simulated numerically using the pseudo-spectral method. The initial perturbations consisted of the two-dimensional fundamental wave and the streamwise-invariant three-dimensional disturbance. A comparison of the formations of the streamwise vortices with different amplitude functions for three-dimensional disturbances was made. In one case the results are similar to that of Rogers and Moser (1992), whereas a different way in which the quadrupole forms and sudden expansion of the rib were observed in another case. The simulation also confirms that stretching by the forming roller rather than Rayleigh centrifugal instability is responsible for the formation of the rib. Finally, numerical flow visualization results were presented. (Edited author abstract) 9 Refs.展开更多
Direct numerical simulation of a jet issuing from a nozzle having a rectangular cross-section is conducted. The vortex in cell (VIC) method, of which computational accuracy was heightened by the authors in a prior stu...Direct numerical simulation of a jet issuing from a nozzle having a rectangular cross-section is conducted. The vortex in cell (VIC) method, of which computational accuracy was heightened by the authors in a prior study, is used for the DNS. The aspect ratio of the nozzle cross-section is 15, and the Reynolds number based on the shorter side length of the nozzle exit is 6700. The turbulence statics, such as the mean velocity and the turbulence intensity, are favorably compared with the experimentally measured results. The behavior of the large-scale eddies as well as the development of the turbulent flow is also confirmed to agree with the measurement. These indicate that the authors’ VIC method is successfully employed for the DNS of rectangular jet.展开更多
Influenced by the fact that vorticity represents rotation for rigid body,people believe this idea also works for fluid flow.However,the vortex predictions by vorticity do not match experimental results,which drove sci...Influenced by the fact that vorticity represents rotation for rigid body,people believe this idea also works for fluid flow.However,the vortex predictions by vorticity do not match experimental results,which drove scientists to look for more appropriate methods to identify vortex.All vortex identification methods can be categorized into three generations.The vorticity-based method is classified as the first generation.Methods relying on eigenvalues of velocity gradient tensor are considered as the second generation.People still believe vorticity is vortex since vorticity theory looks correct in mathematics,but all other methods are only scalars and unable to indicate the swirl direction.Recently,a new vortex identification method called Liutex is innovated.It is regarded as the third-generation method,not only overcoming all previous methods’drawbacks but also having a clear physical meaning.The direction of Liutex represents the swirl axis of rotation,and its strength is equal to twice the angular speed.In this paper,we did a correlation analysis between vorticity,Q,λ_(ci),λ_(2)methods and Liutex based on a direct numerical simulation(DNS)case of boundary layer transition.The results show that the correlation between vorticity and Liutex is very small or even negative in strong shear regions,which demonstrates that using vorticity to detect vortex lacks scientific foundation and vorticity is not appropriate to represent vortex.The correlation analysis also shows that the second generation is contaminated too by shear and thus is not accurate to identify the vortex structure.展开更多
In this paper, a Fourier-Chebyshev pseudospectral scheme with mixed filtering is proposed for three-dimensional vorticity equation. The generalized stability and convergence are proved. The numerical results show the ...In this paper, a Fourier-Chebyshev pseudospectral scheme with mixed filtering is proposed for three-dimensional vorticity equation. The generalized stability and convergence are proved. The numerical results show the advantages of this method.展开更多
A Fourier-Chebyshev spectral scheme is constructed for a three-dimensional vorticity equation. The generalized stability and convergence are proved strictly.
The pseudospectral method for solving vorticity equations on spherical surface is discussed. An interpolation procedure, which is different from the usual onesl is proposed. Based on such an interpolation, the pseudos...The pseudospectral method for solving vorticity equations on spherical surface is discussed. An interpolation procedure, which is different from the usual onesl is proposed. Based on such an interpolation, the pseudospectral scheme is constructed. Its generalized stability and convergence are analyzed rigorously. The theoretical analysis and computational skills can also be applied to other nonlinear partial differential equations defined on spherical surface.展开更多
In this paper we introduce the convective vorticity vector and its application in the forecast and diagnosis of rainstorm.Convective vorticity vector is a parameter of vector field,different from scalar field,it conta...In this paper we introduce the convective vorticity vector and its application in the forecast and diagnosis of rainstorm.Convective vorticity vector is a parameter of vector field,different from scalar field,it contains more important information of physical quantities,so it could not be replaced.Considering the irresistible importance of vector field we will introduce the theory of vector field and its dynamic forecast method.With the convective vorticity vector and its vertical component's tendency equation,diagnostic analysis on the heavy-rainfall event caused by landfall typhoon“Morakot”in the year 2009 is conducted.The result shows that,the abnormal values of convective vorticity vector always changes with the development of the observed precipitation region,and their horizontal distribution is quite similar.Analysis reveals a certain correspondence between the convective vorticity vector and the observed 6-h accumulated surface rainfall,they are significantly related.The convective vorticity vector is capable of describing the typical vertical structure of dynamical and thermodynamic fields of precipitation system,so it is closely related to the occurrence and development of precipitation system and could have certain relation with the surface rainfall regions.展开更多
In this paper, we construct a spectral-finite element scheme for solving semi-periodical two-dimensional vorticity equations. The error between the genuine solution and approximate solutionis estimated strictly. The n...In this paper, we construct a spectral-finite element scheme for solving semi-periodical two-dimensional vorticity equations. The error between the genuine solution and approximate solutionis estimated strictly. The numerical results show the advantages of such a method. The techniqueused in this paper can be easily generalized to three-dimensional problems.展开更多
基金Foundation item:the Natural Science Foundation of Jiangsu Province(BK97056109)
文摘A vorticity-velocity method was used to study the incompressible viscous fluid flow around a circular cylinder with surface suction or blowing. The resulted high order implicit difference equations were effeciently solved by the modified incomplete LU decomposition conjugate gradient scheme ( MILU-CG). The effects of surface suction or blowing' s position and strength on the vortex structures in the cylinder wake, as well as on the drag and lift forces at Reynoldes number Re = 100 were investigated numerically. The results show that the suction on the shoulder of the cylinder or the blowing on the rear of the cylinder can effeciently suppress the asymmetry of the vortex wake in the transverse direction and greatly reduce the lift force; the suction on the shoulder of the cylinder, when its strength is properly chosen, can reduce the drag force significantly, too.
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supported by the Guangdong Basic and Applied Basic Research Foundation(Grant No.2023A1515110198)the Natural Science Foundation of Guangdong Province,China(Grant Nos.2024A1515030131 and 2021A1515010214)+2 种基金the National Natural Science Foundation of China(Grant Nos.12274077,11905032,and 12475014)the Research Fund of the Guangdong-Hong Kong-Macao Joint Laboratory for Intelligent Micro-Nano Optoelectronic Technology(Grant No.2020B1212030010)the Israel Science Foundation(Grant No.1695/22).
文摘We investigate the ground states of spin-orbit coupled spin-1 Bose-Einstein condensates in the presence of Zeeman splitting.By introducing the generalized momentum operator,the linear version of the system is solved exactly,yielding a set of Bessel vortices.Additionally,based on linear solution and using variational approximation,the solutions for the full nonlinear system and their ground state phase diagrams are derived,including the vortex states with quantum numbers m=0,1,as well as mixed states.In this work,mixed states in spin-1 spin-orbit coupling(SOC)BEC are interpreted for the first time as weighted superpositions of three vortex states.Furthermore,the results also indicate that under strong Zeeman splitting,the system cannot form localized states.The variational solutions align well with numerical simulations,showing stable evolution and meeting the criteria for long-term observation in experiments.
基金supported by the National Basic Research Program of China (2005CB321701)NSF of mathematics research special fund of Hebei Province(08M005)
文摘The purpose of this article is to develop and analyze least-squares approximations for the incompressible magnetohydrodynamic equations. The major advantage of the least-squares finite element method is that it is not subjected to the so-called Ladyzhenskaya-Babuska-Brezzi （LBB） condition. The authors employ least-squares functionals which involve a discrete inner product which is related to the inner product in H^-1（Ω）.
基金The project supported by the Zhejiang Province Natural Science Special Fund for Youth Scientists' Cultivation.
文摘The evolution of the three-dimensional time-developing mixing layer was simulated numerically using the pseudo-spectral method. The initial perturbations consisted of the two-dimensional fundamental wave and the streamwise-invariant three-dimensional disturbance. A comparison of the formations of the streamwise vortices with different amplitude functions for three-dimensional disturbances was made. In one case the results are similar to that of Rogers and Moser (1992), whereas a different way in which the quadrupole forms and sudden expansion of the rib were observed in another case. The simulation also confirms that stretching by the forming roller rather than Rayleigh centrifugal instability is responsible for the formation of the rib. Finally, numerical flow visualization results were presented. (Edited author abstract) 9 Refs.
文摘Direct numerical simulation of a jet issuing from a nozzle having a rectangular cross-section is conducted. The vortex in cell (VIC) method, of which computational accuracy was heightened by the authors in a prior study, is used for the DNS. The aspect ratio of the nozzle cross-section is 15, and the Reynolds number based on the shorter side length of the nozzle exit is 6700. The turbulence statics, such as the mean velocity and the turbulence intensity, are favorably compared with the experimentally measured results. The behavior of the large-scale eddies as well as the development of the turbulent flow is also confirmed to agree with the measurement. These indicate that the authors’ VIC method is successfully employed for the DNS of rectangular jet.
文摘Influenced by the fact that vorticity represents rotation for rigid body,people believe this idea also works for fluid flow.However,the vortex predictions by vorticity do not match experimental results,which drove scientists to look for more appropriate methods to identify vortex.All vortex identification methods can be categorized into three generations.The vorticity-based method is classified as the first generation.Methods relying on eigenvalues of velocity gradient tensor are considered as the second generation.People still believe vorticity is vortex since vorticity theory looks correct in mathematics,but all other methods are only scalars and unable to indicate the swirl direction.Recently,a new vortex identification method called Liutex is innovated.It is regarded as the third-generation method,not only overcoming all previous methods’drawbacks but also having a clear physical meaning.The direction of Liutex represents the swirl axis of rotation,and its strength is equal to twice the angular speed.In this paper,we did a correlation analysis between vorticity,Q,λ_(ci),λ_(2)methods and Liutex based on a direct numerical simulation(DNS)case of boundary layer transition.The results show that the correlation between vorticity and Liutex is very small or even negative in strong shear regions,which demonstrates that using vorticity to detect vortex lacks scientific foundation and vorticity is not appropriate to represent vortex.The correlation analysis also shows that the second generation is contaminated too by shear and thus is not accurate to identify the vortex structure.
文摘In this paper, a Fourier-Chebyshev pseudospectral scheme with mixed filtering is proposed for three-dimensional vorticity equation. The generalized stability and convergence are proved. The numerical results show the advantages of this method.
文摘A Fourier-Chebyshev spectral scheme is constructed for a three-dimensional vorticity equation. The generalized stability and convergence are proved strictly.
文摘The pseudospectral method for solving vorticity equations on spherical surface is discussed. An interpolation procedure, which is different from the usual onesl is proposed. Based on such an interpolation, the pseudospectral scheme is constructed. Its generalized stability and convergence are analyzed rigorously. The theoretical analysis and computational skills can also be applied to other nonlinear partial differential equations defined on spherical surface.
基金supported by the Key Project of National Natural Science Foundation of China(41930972)the key special projects plan in key areas of Guangdong Province(2019B111101002)+2 种基金National Natural Sciences General Foundations of China(Grant Nos.41875056)China Meteorological Administration forecaster project(cmayby2019-143)the National Natural Science Foundation of China of China(Grant Nos.41405049).
文摘In this paper we introduce the convective vorticity vector and its application in the forecast and diagnosis of rainstorm.Convective vorticity vector is a parameter of vector field,different from scalar field,it contains more important information of physical quantities,so it could not be replaced.Considering the irresistible importance of vector field we will introduce the theory of vector field and its dynamic forecast method.With the convective vorticity vector and its vertical component's tendency equation,diagnostic analysis on the heavy-rainfall event caused by landfall typhoon“Morakot”in the year 2009 is conducted.The result shows that,the abnormal values of convective vorticity vector always changes with the development of the observed precipitation region,and their horizontal distribution is quite similar.Analysis reveals a certain correspondence between the convective vorticity vector and the observed 6-h accumulated surface rainfall,they are significantly related.The convective vorticity vector is capable of describing the typical vertical structure of dynamical and thermodynamic fields of precipitation system,so it is closely related to the occurrence and development of precipitation system and could have certain relation with the surface rainfall regions.
文摘In this paper, we construct a spectral-finite element scheme for solving semi-periodical two-dimensional vorticity equations. The error between the genuine solution and approximate solutionis estimated strictly. The numerical results show the advantages of such a method. The techniqueused in this paper can be easily generalized to three-dimensional problems.
