In Multi-user MIMO (MU-MIMO) downlink system, suitable user selection schemes can improve spatial diversity gain. In most of previous studies, it is always assumed that the base station (BS) knows full channel state i...In Multi-user MIMO (MU-MIMO) downlink system, suitable user selection schemes can improve spatial diversity gain. In most of previous studies, it is always assumed that the base station (BS) knows full channel state information (CSI) of each user, which does not consider the reality. However, there are only limited feedback bits in real system. Besides, user fairness is often ignored in most of current user selection schemes. To discuss the user fairness and limited feedback, in this paper, the user selection scheme with limited feedback bits is proposed. The BS utilizes codebook precoding transmitting strategy with LTE codebook. Furthermore, this paper analyzes the influence of the number of feedback bits and the number of users on user fairness and system sum capacity. Simulation results show that in order to achieve better user fairness, we can use fewer bits for feedback CSI when the number of user is small, and more feedback bits when the number of users is large.展开更多
A two-dimensional （2D） dam-break flow numerical model was developed based on the finite-volume total variation diminishing （TVD） and monotone upstream-centered scheme for conservation laws （MUSCL）-Hancock scheme...A two-dimensional （2D） dam-break flow numerical model was developed based on the finite-volume total variation diminishing （TVD） and monotone upstream-centered scheme for conservation laws （MUSCL）-Hancock scheme, which has second-order accuracy in both time and space. A Harten-Lax-van Leer-contact （HLLC） approximate Riemann solver was used to evaluate fluxes. The TVD MUSCL-Hancock numerical scheme utilizes slope limiters, such as the minmod, double minmod, superbee, van Albada, and van Leer limiters, to prevent spurious oscillations and maintain monotonicity near discontinuities. A comparative study of the impact of various slope limiters on the accuracy of the numerical flow model was conducted with several dam-break examples including wet and dry bed cases. The numerical results of the superbee and double minmod limiters agree better with the theoretical solution and have higher accuracy than other limiters in one-dimensional （1D） space. The ratio of the downstream water depth to the upstream water depth was used to select the proper slope limiter. For the 2D numerical model, the superbee limiter should not be used, owing to significant numerical dispersion.展开更多
The Vlasov-Poisson-Fokker-Planck system under the high field scaling describes the Brownian motion of a large system of particles in a surrounding bath where both collision and field effects （electrical or gravitatio...The Vlasov-Poisson-Fokker-Planck system under the high field scaling describes the Brownian motion of a large system of particles in a surrounding bath where both collision and field effects （electrical or gravitational） are dominant. Numerically solving this system becomes challenging due to the stiff collision term and stiff nonlinear transport term with respect to the high field. We present a class of Asymptotic-Preserving scheme which is efficient in the high field regime, namely, large time steps and coarse meshes can be used, yet the high field limit is still captured. The idea is to combine the two stiff terms and treat them implicitly. Thanks to the linearity of the collision term, using the discretization described in [Jin S, Yah B. J. Comp. Phys., 2011, 230： 6420-6437] we only need to invert a symmetric matrix. This method can be easily extended to higher dimensions. The method is shown to be positive, stable, mass and asymptotic preserving. Numerical experiments validate its efficiency in both kinetic and high field regimes including mixing regimes.展开更多
According to the Liu's weighted idea, a space third-order WNND (weighted non-oscillatory, containing no free parameters, and dissipative scheme) scheme was constructed based on the stencils of second-order NND (no...According to the Liu's weighted idea, a space third-order WNND (weighted non-oscillatory, containing no free parameters, and dissipative scheme) scheme was constructed based on the stencils of second-order NND (non-oscillatory, containing no free parameters, and dissipative scheme) scheme. It was applied in solving linear-wave equation, 1D Euler equations and 3D Navier-Stokes equations. The numerical results indicate that the WNND scheme which does not increase interpolated point(compared to NND scheme) has more advantages in simulating discontinues and convergence than NND scheme. Appling WNND scheme to simulating the hypersonic flow around lift-body shows:With the AoA(angle of attack) increasing from 0° to 50°, the structure of limiting streamline of leeward surface changes from unseparating,open-separating to separating, which occurs from the combined-point (which consists of saddle and node points). The separating area of upper wing surface is increasing with the (AoA's) increasing. The topological structures of hypersonic flowfield based on the sectional flow patterns perpendicular to the body axis agree well with Zhang Hanxin's theory. Additionally, the unstable-structure phenomenon which is showed by two saddles connection along leeward symmetry line occurs at some sections when the AoA is bigger than 20°.展开更多
In most TVD schemes, the r-factors were proposed according to the cell-centered（CC） finite volume method（FVM） framework for the numerical approximation to the convective term. However, it is questionable whether t...In most TVD schemes, the r-factors were proposed according to the cell-centered（CC） finite volume method（FVM） framework for the numerical approximation to the convective term. However, it is questionable whether those r-factors would be appropriate and effective for the vertex-centered（VC） FVM. In the paper, we collected five kinds of r-factor formulae and found out that only three of those, respectively by Bruner（1996）, Darwish and Moukalled（2003） and Cassuli and Zanolli（2005） can be formally extended to a context of the VC FVM. Numerical tests indicate that the TVD schemes and r-factors, after being extended and introduced to a context of the VC FVM, maintained their similar characteristics as in a context of the CC FVM. However, when the gradient-based r-factors and the SUPERBEE scheme were applied simultaneously, non-physical oscillations near the sharp step would appear. In the transient case, the oscillations were weaker in a context of the VC FVM than those in a context of the CC FVM, while the effect was reversed in the steady case. To eliminate disadvantages in the gradient-based r-factor formula, a new modification method by limiting values on the virtual node, namely Фu in the paper, was validated by the tests to effectively dissipate spurious oscillations.展开更多
针对构网型变流器(grid-forming voltage source converter,GFM-VSC)系统在大扰动下暂态稳定问题,现有研究未能充分考虑电力电子电源暂态快速响应与控制可塑的特点。为此,以GFM-VSC为对象,借助等面积法原理与相平面图法,从能量角度揭示...针对构网型变流器(grid-forming voltage source converter,GFM-VSC)系统在大扰动下暂态稳定问题,现有研究未能充分考虑电力电子电源暂态快速响应与控制可塑的特点。为此,以GFM-VSC为对象,借助等面积法原理与相平面图法,从能量角度揭示了其暂态响应机制与传统同步机系统的差异,分析了控制塑造下GFM-VSC系统的暂态稳定机理;然后,针对大扰动下易于触发的限幅环节,分析了系统无法自主退出限幅而失稳的机制,并提出了附带电流分配系数的改进限幅策略,有效增强了系统暂态稳定性。最后,通过仿真验证了理论分析与改进方法的正确性。展开更多
文摘In Multi-user MIMO (MU-MIMO) downlink system, suitable user selection schemes can improve spatial diversity gain. In most of previous studies, it is always assumed that the base station (BS) knows full channel state information (CSI) of each user, which does not consider the reality. However, there are only limited feedback bits in real system. Besides, user fairness is often ignored in most of current user selection schemes. To discuss the user fairness and limited feedback, in this paper, the user selection scheme with limited feedback bits is proposed. The BS utilizes codebook precoding transmitting strategy with LTE codebook. Furthermore, this paper analyzes the influence of the number of feedback bits and the number of users on user fairness and system sum capacity. Simulation results show that in order to achieve better user fairness, we can use fewer bits for feedback CSI when the number of user is small, and more feedback bits when the number of users is large.
基金supported by the National Natural Science Foundation of China(Grants No.51679170,51379157,and 51439007)
文摘A two-dimensional （2D） dam-break flow numerical model was developed based on the finite-volume total variation diminishing （TVD） and monotone upstream-centered scheme for conservation laws （MUSCL）-Hancock scheme, which has second-order accuracy in both time and space. A Harten-Lax-van Leer-contact （HLLC） approximate Riemann solver was used to evaluate fluxes. The TVD MUSCL-Hancock numerical scheme utilizes slope limiters, such as the minmod, double minmod, superbee, van Albada, and van Leer limiters, to prevent spurious oscillations and maintain monotonicity near discontinuities. A comparative study of the impact of various slope limiters on the accuracy of the numerical flow model was conducted with several dam-break examples including wet and dry bed cases. The numerical results of the superbee and double minmod limiters agree better with the theoretical solution and have higher accuracy than other limiters in one-dimensional （1D） space. The ratio of the downstream water depth to the upstream water depth was used to select the proper slope limiter. For the 2D numerical model, the superbee limiter should not be used, owing to significant numerical dispersion.
基金supported by NSF grant No.DMS-0608720,and NSF FRG grant DMS-0757285
文摘The Vlasov-Poisson-Fokker-Planck system under the high field scaling describes the Brownian motion of a large system of particles in a surrounding bath where both collision and field effects （electrical or gravitational） are dominant. Numerically solving this system becomes challenging due to the stiff collision term and stiff nonlinear transport term with respect to the high field. We present a class of Asymptotic-Preserving scheme which is efficient in the high field regime, namely, large time steps and coarse meshes can be used, yet the high field limit is still captured. The idea is to combine the two stiff terms and treat them implicitly. Thanks to the linearity of the collision term, using the discretization described in [Jin S, Yah B. J. Comp. Phys., 2011, 230： 6420-6437] we only need to invert a symmetric matrix. This method can be easily extended to higher dimensions. The method is shown to be positive, stable, mass and asymptotic preserving. Numerical experiments validate its efficiency in both kinetic and high field regimes including mixing regimes.
文摘According to the Liu's weighted idea, a space third-order WNND (weighted non-oscillatory, containing no free parameters, and dissipative scheme) scheme was constructed based on the stencils of second-order NND (non-oscillatory, containing no free parameters, and dissipative scheme) scheme. It was applied in solving linear-wave equation, 1D Euler equations and 3D Navier-Stokes equations. The numerical results indicate that the WNND scheme which does not increase interpolated point(compared to NND scheme) has more advantages in simulating discontinues and convergence than NND scheme. Appling WNND scheme to simulating the hypersonic flow around lift-body shows:With the AoA(angle of attack) increasing from 0° to 50°, the structure of limiting streamline of leeward surface changes from unseparating,open-separating to separating, which occurs from the combined-point (which consists of saddle and node points). The separating area of upper wing surface is increasing with the (AoA's) increasing. The topological structures of hypersonic flowfield based on the sectional flow patterns perpendicular to the body axis agree well with Zhang Hanxin's theory. Additionally, the unstable-structure phenomenon which is showed by two saddles connection along leeward symmetry line occurs at some sections when the AoA is bigger than 20°.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.41306078 and 41301414)the National Engineering Research Center for Inland Waterway Regulation and Key Laboratory of Hydraulic and Waterway Engineering of the Ministry of Education Program(Grant No.SLK2016B03)the Key Laboratory of the Inland Waterway Regulation of the Ministry of Transportation Program(Grant No.NHHD-201514)
文摘In most TVD schemes, the r-factors were proposed according to the cell-centered（CC） finite volume method（FVM） framework for the numerical approximation to the convective term. However, it is questionable whether those r-factors would be appropriate and effective for the vertex-centered（VC） FVM. In the paper, we collected five kinds of r-factor formulae and found out that only three of those, respectively by Bruner（1996）, Darwish and Moukalled（2003） and Cassuli and Zanolli（2005） can be formally extended to a context of the VC FVM. Numerical tests indicate that the TVD schemes and r-factors, after being extended and introduced to a context of the VC FVM, maintained their similar characteristics as in a context of the CC FVM. However, when the gradient-based r-factors and the SUPERBEE scheme were applied simultaneously, non-physical oscillations near the sharp step would appear. In the transient case, the oscillations were weaker in a context of the VC FVM than those in a context of the CC FVM, while the effect was reversed in the steady case. To eliminate disadvantages in the gradient-based r-factor formula, a new modification method by limiting values on the virtual node, namely Фu in the paper, was validated by the tests to effectively dissipate spurious oscillations.
文摘针对构网型变流器(grid-forming voltage source converter,GFM-VSC)系统在大扰动下暂态稳定问题,现有研究未能充分考虑电力电子电源暂态快速响应与控制可塑的特点。为此,以GFM-VSC为对象,借助等面积法原理与相平面图法,从能量角度揭示了其暂态响应机制与传统同步机系统的差异,分析了控制塑造下GFM-VSC系统的暂态稳定机理;然后,针对大扰动下易于触发的限幅环节,分析了系统无法自主退出限幅而失稳的机制,并提出了附带电流分配系数的改进限幅策略,有效增强了系统暂态稳定性。最后,通过仿真验证了理论分析与改进方法的正确性。
