Mixed finite element methods are considered for a ferrofluid flow model with magnetization paralleled to the magnetic field.The ferrofluid model is a coupled system of the Maxwell equations and the incompressible Navi...Mixed finite element methods are considered for a ferrofluid flow model with magnetization paralleled to the magnetic field.The ferrofluid model is a coupled system of the Maxwell equations and the incompressible Navier-Stokes equations.By skillfully introducing some new variables,the model is rewritten as several decoupled subsystems that can be solved independently.Mixed finite element formulations are given to discretize the decoupled systems with proper finite element spaces.Existence and uniqueness of the mixed finite element solutions are shown,and optimal order error estimates are obtained under some reasonable assumptions.Numerical experiments confirm the theoretical results.展开更多
Presents an h -- p finite element methods based upon a mixed variational formulation for the three-field Stokes equations and linearized Non-Newtonian flow. Computation of the algebraic system generated from Problem H...Presents an h -- p finite element methods based upon a mixed variational formulation for the three-field Stokes equations and linearized Non-Newtonian flow. Computation of the algebraic system generated from Problem H[sub h]; Methodology; Results and discussion.展开更多
In this paper we propose a characteristics mixed finite element method to overcome thenumerical dispersion for the 2-phase immiscible displacement. The pressure and associatedfluid velocity will be approximated by a m...In this paper we propose a characteristics mixed finite element method to overcome thenumerical dispersion for the 2-phase immiscible displacement. The pressure and associatedfluid velocity will be approximated by a mixed finite element method, and the saturationwill be treated by a backward characteristics method. The L_∞ stability and convergence forthe scheme are proved, and optimal-order error estimates in L_∞ are obtained.展开更多
The cement mixing (CM) pile is a common method of improving soft offshore ground. The strength growth of CM piles under complex conditions is affected by many factors, especially the cement and moisture contents, and ...The cement mixing (CM) pile is a common method of improving soft offshore ground. The strength growth of CM piles under complex conditions is affected by many factors, especially the cement and moisture contents, and shows significant uncertainty. To investigate the stochasticity of the early strength of CM piles and its impact on the displacement and stability of a seawall, a series of laboratory tests and numerical analyses were carried out in this study. Vane shear tests were conducted on the cement-solidified soil to determine the relationships between the undrained shear strength s_(u) of the cement soil curing in the seawater and the cement content a_(c), as well as the in situ soil moisture content w. It can be inferred that the 24 h undrained shear strength follows a normal distribution. A numerical model considering the random CM pile strength was established to investigate the deformation of the seawall. Due to the uncertainty of CM pile strength, the displacement of the seawall demonstrates a certain discreteness. The decrease of the mean undrained shear strength of CM piles causes a corresponding increase in the average displacement of the seawall. When the mean strength of CM piles is lower than a certain threshold, there is a risk of instability. Furthermore, the heterogeneity of the strength within an individual CM pile also has an impact on seawall displacement. Attention should be paid to the uncertainty of CM pile strength to control displacement and stability.展开更多
The operator splitting method is used to deal with the Navier-Stokes equation, in which the physical process described by the equation is decomposed into two processes： a diffusion process and a convection process; a...The operator splitting method is used to deal with the Navier-Stokes equation, in which the physical process described by the equation is decomposed into two processes： a diffusion process and a convection process; and the finite element equation is established. The velocity field in the element is described by the shape function of the isoparametric element with nine nodes and the pressure field is described by the interpolation function of the four nodes at the vertex of the isoparametric element with nine nodes. The subroutine of the element and the integrated finite element code are generated by the Finite Element Program Generator （FEPG） successfully. The numerical simulation about the incompressible viscous liquid flowing over a cylinder is carded out. The solution agrees with the experimental results very well.展开更多
This paper develops a posteriori error estimates of residual type for conforming and mixed finite element approximations of the fourth order Cahn-Hilliard equation ut ＋ △（ε△Au-ε^-1f（u）） = 0. It is shown that ...This paper develops a posteriori error estimates of residual type for conforming and mixed finite element approximations of the fourth order Cahn-Hilliard equation ut ＋ △（ε△Au-ε^-1f（u）） = 0. It is shown that the a posteriori error bounds depends on ε^-1 only in some low polynomial order, instead of exponential order. Using these a posteriori error estimates, we construct at2 adaptive algorithm for computing the solution of the Cahn- Hilliard equation and its sharp interface limit, the Hele-Shaw flow. Numerical experiments are presented to show the robustness and effectiveness of the new error estimators and the proposed adaptive algorithm.展开更多
特高压直流(UHVDC)输电线路地面离子流场的大小是检验电磁环境是否超标的重要判据,对不同风速条件下的地面离子流场的分布进行了计算研究。针对离子流场的计算,提出一种改进迭代上流有限元方法,建立了考虑风速影响的离子流场模型。研究...特高压直流(UHVDC)输电线路地面离子流场的大小是检验电磁环境是否超标的重要判据,对不同风速条件下的地面离子流场的分布进行了计算研究。针对离子流场的计算,提出一种改进迭代上流有限元方法,建立了考虑风速影响的离子流场模型。研究了不同风速对±800 k V输电线路离子流场分布规律的影响。研究表明,地面最大合成场强和离子流密度随风速的增大而增加明显,且风速会使其发生一定偏移。考虑风速为8 m/s时,地面最大合成场强比无风增加了12.64 k V/m,且地面最大离子流密度是无风时的2.65倍。水平风速越大地面合成场强和离子流密度的分布曲线和峰值往背风向偏移越严重,空间其他较远处的合成场强和电荷密度变化不大,且空间合成场强与电荷密度的最大值主要分布于导线周围空间。展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.11971094,12171340).
文摘Mixed finite element methods are considered for a ferrofluid flow model with magnetization paralleled to the magnetic field.The ferrofluid model is a coupled system of the Maxwell equations and the incompressible Navier-Stokes equations.By skillfully introducing some new variables,the model is rewritten as several decoupled subsystems that can be solved independently.Mixed finite element formulations are given to discretize the decoupled systems with proper finite element spaces.Existence and uniqueness of the mixed finite element solutions are shown,and optimal order error estimates are obtained under some reasonable assumptions.Numerical experiments confirm the theoretical results.
文摘Presents an h -- p finite element methods based upon a mixed variational formulation for the three-field Stokes equations and linearized Non-Newtonian flow. Computation of the algebraic system generated from Problem H[sub h]; Methodology; Results and discussion.
基金Project supported by the National Natural Science Foundation of China.
文摘In this paper we propose a characteristics mixed finite element method to overcome thenumerical dispersion for the 2-phase immiscible displacement. The pressure and associatedfluid velocity will be approximated by a mixed finite element method, and the saturationwill be treated by a backward characteristics method. The L_∞ stability and convergence forthe scheme are proved, and optimal-order error estimates in L_∞ are obtained.
基金supported by the Finance Science and Technology Project of Hainan Province(No.ZDKJ202019)the Key Research and Development Program of Zhejiang Province(No.2021C03014)the Natural Science Foundation of Zhejiang Province(No.LR22E080005),China.
文摘The cement mixing (CM) pile is a common method of improving soft offshore ground. The strength growth of CM piles under complex conditions is affected by many factors, especially the cement and moisture contents, and shows significant uncertainty. To investigate the stochasticity of the early strength of CM piles and its impact on the displacement and stability of a seawall, a series of laboratory tests and numerical analyses were carried out in this study. Vane shear tests were conducted on the cement-solidified soil to determine the relationships between the undrained shear strength s_(u) of the cement soil curing in the seawater and the cement content a_(c), as well as the in situ soil moisture content w. It can be inferred that the 24 h undrained shear strength follows a normal distribution. A numerical model considering the random CM pile strength was established to investigate the deformation of the seawall. Due to the uncertainty of CM pile strength, the displacement of the seawall demonstrates a certain discreteness. The decrease of the mean undrained shear strength of CM piles causes a corresponding increase in the average displacement of the seawall. When the mean strength of CM piles is lower than a certain threshold, there is a risk of instability. Furthermore, the heterogeneity of the strength within an individual CM pile also has an impact on seawall displacement. Attention should be paid to the uncertainty of CM pile strength to control displacement and stability.
文摘The operator splitting method is used to deal with the Navier-Stokes equation, in which the physical process described by the equation is decomposed into two processes： a diffusion process and a convection process; and the finite element equation is established. The velocity field in the element is described by the shape function of the isoparametric element with nine nodes and the pressure field is described by the interpolation function of the four nodes at the vertex of the isoparametric element with nine nodes. The subroutine of the element and the integrated finite element code are generated by the Finite Element Program Generator （FEPG） successfully. The numerical simulation about the incompressible viscous liquid flowing over a cylinder is carded out. The solution agrees with the experimental results very well.
基金the NSF grants DMS-0410266 and DMS-0710831the China National Basic Research Program under the grant 2005CB321701+1 种基金the Program for the New Century Outstanding Talents in Universities of Chinathe Natural Science Foundation of Jiangsu Province under the grant BK2006511
文摘This paper develops a posteriori error estimates of residual type for conforming and mixed finite element approximations of the fourth order Cahn-Hilliard equation ut ＋ △（ε△Au-ε^-1f（u）） = 0. It is shown that the a posteriori error bounds depends on ε^-1 only in some low polynomial order, instead of exponential order. Using these a posteriori error estimates, we construct at2 adaptive algorithm for computing the solution of the Cahn- Hilliard equation and its sharp interface limit, the Hele-Shaw flow. Numerical experiments are presented to show the robustness and effectiveness of the new error estimators and the proposed adaptive algorithm.
文摘特高压直流(UHVDC)输电线路地面离子流场的大小是检验电磁环境是否超标的重要判据,对不同风速条件下的地面离子流场的分布进行了计算研究。针对离子流场的计算,提出一种改进迭代上流有限元方法,建立了考虑风速影响的离子流场模型。研究了不同风速对±800 k V输电线路离子流场分布规律的影响。研究表明,地面最大合成场强和离子流密度随风速的增大而增加明显,且风速会使其发生一定偏移。考虑风速为8 m/s时,地面最大合成场强比无风增加了12.64 k V/m,且地面最大离子流密度是无风时的2.65倍。水平风速越大地面合成场强和离子流密度的分布曲线和峰值往背风向偏移越严重,空间其他较远处的合成场强和电荷密度变化不大,且空间合成场强与电荷密度的最大值主要分布于导线周围空间。
