Based on the low-order conforming finite element subspace （Vh, Mh） such as the P1-P0 triangle element or the Q1-P0 quadrilateral element, the locally stabilized finite element method for the Stokes problem with nonl...Based on the low-order conforming finite element subspace （Vh, Mh） such as the P1-P0 triangle element or the Q1-P0 quadrilateral element, the locally stabilized finite element method for the Stokes problem with nonlinear slip boundary conditions is investigated in this paper. For this class of nonlinear slip boundary conditions including the subdifferential property, the weak variational formulation associated with the Stokes problem is an variational inequality. Since （Vh, Mh） does not satisfy the discrete inf-sup conditions, a macroelement condition is introduced for constructing the locally stabilized formulation such that the stability of （Vh, Mh） is established. Under these conditions, we obtain the H1 and L2 error estimates for the numerical solutions.展开更多
In the paper,an inf-sup stabilized finite element method by multiscale functions for the Stokes equations is discussed.The key idea is to use a PetrovGalerkin approach based on the enrichment of the standard polynomi...In the paper,an inf-sup stabilized finite element method by multiscale functions for the Stokes equations is discussed.The key idea is to use a PetrovGalerkin approach based on the enrichment of the standard polynomial space for the velocity component with multiscale functions.The inf-sup condition for P_(1)-P_(0)triangular element(or Q_(1)-P_(0)quadrilateral element)is established.The optimal error estimates of the stabilized finite element method for the Stokes equations are obtained.展开更多
In this paper,a stabilized finite element technique,actualized by streamline upwind Petrov-Galerkin(SUPG) stabilized method and three-step finite element method(FEM),for large eddy simulation(LES) is developed to pred...In this paper,a stabilized finite element technique,actualized by streamline upwind Petrov-Galerkin(SUPG) stabilized method and three-step finite element method(FEM),for large eddy simulation(LES) is developed to predict the wind flow with high Reynolds numbers.Weak form of LES motion equation is combined with the SUPG stabilized term for the spatial finite element discretization.An explicit three-step scheme is implemented for the temporal discretization.For the numerical example of 2D wind flow over a square rib at Re=4.2×105,the Smagorinsky's subgrid-scale(SSGS) model,the DSGS model,and the DSGS model with Cabot near-wall model are applied,and their results are analyzed and compared with experimental results.Furthermore,numerical examples of 3D wind flow around a surface-mounted cube with different Reynolds numbers are performed using DSGS model with Cabot near-wall model based on the present stabilized method to study the wind field and compared with experimental and numerical results.Finally,vortex structures for wind flow around a surface-mounted cube are studied by present numerical method.Stable and satisfactory results are obtained,which are consistent with most of the measurements even under coarse mesh.展开更多
This paper is devoted to the establishment of sharper a priori stability and error estimates of a stabilized finite element method proposed by Barrenechea and Valentin for solving the generalized Stokes problem,which ...This paper is devoted to the establishment of sharper a priori stability and error estimates of a stabilized finite element method proposed by Barrenechea and Valentin for solving the generalized Stokes problem,which involves a viscosity v and a reaction consta nt a.With the establishmen t of sharper st ability estimates and the help of ad hoc finite element projections,we can explicitly establish the dependence of error bounds of velocity and pressure on the viscosity z/,the reaction constant cr,and the mesh size h.Our analysis reveals that the viscosity y and the reaction constant a respectively act in the numerator position and the denominator position in the error estimates of velocity and pressure in standard norms without any weights.Consequently,the stabilization method is indeed suitable for the generalized Stokes problem with a small viscosity u and a large reaction constant a.The sharper error estimates agree very well with the numerical results.展开更多
A stabilized finite element algorithm potential for wind-structure interaction(WSI) problem is presented in this paper. Streamline upwind Petrov-Galerkin(SUPG) scheme of the large eddy simulation(LES) of dynamic sub-g...A stabilized finite element algorithm potential for wind-structure interaction(WSI) problem is presented in this paper. Streamline upwind Petrov-Galerkin(SUPG) scheme of the large eddy simulation(LES) of dynamic sub-grid scale(DSGS) is developed under the framework of arbitrary Lagrangian-Eulerian(ALE) description to solve the governing equations. High stabilization is achieved by a three-step technique in the temporal discretization. On the other hand, the partitioned procedure is employed for the consideration of the coupled WSI problem. Newmark integral method is introduced for the computation of structure domain, while spring analogy method is used for the grid update of the mesh domain. The developed computational codes are applied to the analysis of wind-induced effect of a spatial latticed structure. The numerical predictions of the three-dimensional wind flow features, the wind pressures and the wind-induced effect of spatial structures are given. Comparisons are made between the effects of rigid structure in view of the WSI.展开更多
Focuses on a study on the development of a stabilized finite element method for solving the advection-diffusion equations with a zero Dirichlet boundary condition. Problem formulation; Error analysis.
Mass movements are very common problems in the eastern Black Sea region of Turkey due to its climate conditions, geological, and geomorphological characteristics. High slope angle, weathering, dense rainfalls, and ant...Mass movements are very common problems in the eastern Black Sea region of Turkey due to its climate conditions, geological, and geomorphological characteristics. High slope angle, weathering, dense rainfalls, and anthropogenic impacts are generally reported as the most important triggering factors in the region. Following the portal slope excavations in the entrance section of Cankurtaran tunnel, located in the region, where the highly weathered andesitic tuff crops out, a circular toe failure occurred. The main target of the present study is to investigate the causes and occurrence mechanism of this failure and to determine the feasible remedial measures against it using finite element method(FEM) in four stages. These stages are slope stability analyses for pre-and postexcavation cases, and remediation design assessments for slope and tunnel. The results of the FEM-SSR analyses indicated that the insufficient initial support design and weathering of the andesitic tuffs are the main factors that caused the portal failure. After installing a rock retaining wall with jet grout columns and reinforced slope benching applications, the factor of safety increased from 0.83 to 2.80. In addition toslope stability evaluation, the Rock Mass Rating(RMR), Rock Mass Quality(Q) and New Austrian Tunneling Method(NATM) systems were also utilized as empirical methods to characterize the tunnel ground and to determine the tunnel support design. The performance of the suggested empirical support design, induced stress distributions and deformations were analyzed by means of numerical modelling. Finally, it was concluded that the recommended stabilization technique was essential for the dynamic long-term stability and prevents the effects of failure. Additionally, the FEM method gives useful and reasonably reliable results in evaluating the stability of cut slopes and tunnels excavated both in continuous and discontinuous rock masses.展开更多
In this work we consider the Reduced Basis method for the solution of parametrized advection-reaction partial differential equations. For the generation of the basis we adopt a stabilized finite element method and we ...In this work we consider the Reduced Basis method for the solution of parametrized advection-reaction partial differential equations. For the generation of the basis we adopt a stabilized finite element method and we define the Reduced Basis method in the ＂primal- dual＂ formulation for this stabilized problem. We provide a priori Reduced Basis error estimates and we discuss the effects of the finite element approximation on the Reduced Basis error. We propose an adaptive algorithm, based on the a posteriori Reduced Basis error estimate, for the selection of the sample sets upon which the basis are built; the idea leading this algorithm is the minimization of the computational costs associated with the solution of the Reduced Basis problem. Numerical tests demonstrate the efficiency, in terms of computational costs, of the ＂primal-dual＂ Reduced Basis approach with respect to an ＂only primal＂ one. Parametrized advection-reaction partial differential equations, Reduced Basis method, ＂primal-dual＂ reduced basis approach, Stabilized finite element method, a posteriori error estimation.展开更多
Based on a new DIY concept for software development, an automatic program-generating technology attached on a software system called as Finite Element Program Generator （FEPG） provides a platform of developing progr...Based on a new DIY concept for software development, an automatic program-generating technology attached on a software system called as Finite Element Program Generator （FEPG） provides a platform of developing programs, through which a scientific researcher can submit his special physico-mathematical problem to the system in a more direct and convenient way for solution. For solving flow and heat problems by using finite element method, the stabilization technologies and fraction-step methods are adopted to overcome the numerical difficul- ties caused mainly due to the dominated convection. A couple of benchmark problems are given in this paper as examples to illustrate the usage and the superiority of the automatic program generation technique, including the flow in a lid-driven cavity, the starting flow in a circular pipe, the natural convection in a square cavity, and the flow past a circular cylinder, etc. They are also shown as the verification of the algorithms.展开更多
基金supported by the National Natural Science Foundation of China(10901122)Zhejiang Provincial Natural Science Foundation (Y6090108)supported by the National Natural Science Foundation of China(10971165)
文摘Based on the low-order conforming finite element subspace （Vh, Mh） such as the P1-P0 triangle element or the Q1-P0 quadrilateral element, the locally stabilized finite element method for the Stokes problem with nonlinear slip boundary conditions is investigated in this paper. For this class of nonlinear slip boundary conditions including the subdifferential property, the weak variational formulation associated with the Stokes problem is an variational inequality. Since （Vh, Mh） does not satisfy the discrete inf-sup conditions, a macroelement condition is introduced for constructing the locally stabilized formulation such that the stability of （Vh, Mh） is established. Under these conditions, we obtain the H1 and L2 error estimates for the numerical solutions.
基金the support of the Natural Science Foundation of China(No.10671154)the National Basic Research Program(No.2005CB321703)。
文摘In the paper,an inf-sup stabilized finite element method by multiscale functions for the Stokes equations is discussed.The key idea is to use a PetrovGalerkin approach based on the enrichment of the standard polynomial space for the velocity component with multiscale functions.The inf-sup condition for P_(1)-P_(0)triangular element(or Q_(1)-P_(0)quadrilateral element)is established.The optimal error estimates of the stabilized finite element method for the Stokes equations are obtained.
基金Project supported by the National Natural Science Foundation of China(No.51078230)the Research Fund for the Doctoral Program of Higher Education of China(No.200802480056)the Key Project of Fund of Science and Technology Development of Shanghai(No.10JC1407900),China
文摘In this paper,a stabilized finite element technique,actualized by streamline upwind Petrov-Galerkin(SUPG) stabilized method and three-step finite element method(FEM),for large eddy simulation(LES) is developed to predict the wind flow with high Reynolds numbers.Weak form of LES motion equation is combined with the SUPG stabilized term for the spatial finite element discretization.An explicit three-step scheme is implemented for the temporal discretization.For the numerical example of 2D wind flow over a square rib at Re=4.2×105,the Smagorinsky's subgrid-scale(SSGS) model,the DSGS model,and the DSGS model with Cabot near-wall model are applied,and their results are analyzed and compared with experimental results.Furthermore,numerical examples of 3D wind flow around a surface-mounted cube with different Reynolds numbers are performed using DSGS model with Cabot near-wall model based on the present stabilized method to study the wind field and compared with experimental and numerical results.Finally,vortex structures for wind flow around a surface-mounted cube are studied by present numerical method.Stable and satisfactory results are obtained,which are consistent with most of the measurements even under coarse mesh.
基金The work of H.Y.Duan was supported by the National Natural Science Foundation of China under grants 11971366,11571266,11661161017,1117116&11071132the Collaborative Innovation Centre of Mat hematics,and the Hubei Key Laboratory of Computational Science(Wuhan University,the Natural Science Foundation of Hubei Province No.2019CFA007).
文摘This paper is devoted to the establishment of sharper a priori stability and error estimates of a stabilized finite element method proposed by Barrenechea and Valentin for solving the generalized Stokes problem,which involves a viscosity v and a reaction consta nt a.With the establishmen t of sharper st ability estimates and the help of ad hoc finite element projections,we can explicitly establish the dependence of error bounds of velocity and pressure on the viscosity z/,the reaction constant cr,and the mesh size h.Our analysis reveals that the viscosity y and the reaction constant a respectively act in the numerator position and the denominator position in the error estimates of velocity and pressure in standard norms without any weights.Consequently,the stabilization method is indeed suitable for the generalized Stokes problem with a small viscosity u and a large reaction constant a.The sharper error estimates agree very well with the numerical results.
基金the National Natural Science Foundation of China(Nos.11172174 and 51278297)the Research Program of Shanghai Leader Talent(No.20)the Doctoral Disciplinary Special Research Project of Chinese Ministry of Education(No.20130073110096)
文摘A stabilized finite element algorithm potential for wind-structure interaction(WSI) problem is presented in this paper. Streamline upwind Petrov-Galerkin(SUPG) scheme of the large eddy simulation(LES) of dynamic sub-grid scale(DSGS) is developed under the framework of arbitrary Lagrangian-Eulerian(ALE) description to solve the governing equations. High stabilization is achieved by a three-step technique in the temporal discretization. On the other hand, the partitioned procedure is employed for the consideration of the coupled WSI problem. Newmark integral method is introduced for the computation of structure domain, while spring analogy method is used for the grid update of the mesh domain. The developed computational codes are applied to the analysis of wind-induced effect of a spatial latticed structure. The numerical predictions of the three-dimensional wind flow features, the wind pressures and the wind-induced effect of spatial structures are given. Comparisons are made between the effects of rigid structure in view of the WSI.
基金the National Natural Science Foundation of China.
文摘Focuses on a study on the development of a stabilized finite element method for solving the advection-diffusion equations with a zero Dirichlet boundary condition. Problem formulation; Error analysis.
文摘Mass movements are very common problems in the eastern Black Sea region of Turkey due to its climate conditions, geological, and geomorphological characteristics. High slope angle, weathering, dense rainfalls, and anthropogenic impacts are generally reported as the most important triggering factors in the region. Following the portal slope excavations in the entrance section of Cankurtaran tunnel, located in the region, where the highly weathered andesitic tuff crops out, a circular toe failure occurred. The main target of the present study is to investigate the causes and occurrence mechanism of this failure and to determine the feasible remedial measures against it using finite element method(FEM) in four stages. These stages are slope stability analyses for pre-and postexcavation cases, and remediation design assessments for slope and tunnel. The results of the FEM-SSR analyses indicated that the insufficient initial support design and weathering of the andesitic tuffs are the main factors that caused the portal failure. After installing a rock retaining wall with jet grout columns and reinforced slope benching applications, the factor of safety increased from 0.83 to 2.80. In addition toslope stability evaluation, the Rock Mass Rating(RMR), Rock Mass Quality(Q) and New Austrian Tunneling Method(NATM) systems were also utilized as empirical methods to characterize the tunnel ground and to determine the tunnel support design. The performance of the suggested empirical support design, induced stress distributions and deformations were analyzed by means of numerical modelling. Finally, it was concluded that the recommended stabilization technique was essential for the dynamic long-term stability and prevents the effects of failure. Additionally, the FEM method gives useful and reasonably reliable results in evaluating the stability of cut slopes and tunnels excavated both in continuous and discontinuous rock masses.
基金support provided thorough the "Progetto Rocca", MIT-Politecnico di Milano collaboration
文摘In this work we consider the Reduced Basis method for the solution of parametrized advection-reaction partial differential equations. For the generation of the basis we adopt a stabilized finite element method and we define the Reduced Basis method in the ＂primal- dual＂ formulation for this stabilized problem. We provide a priori Reduced Basis error estimates and we discuss the effects of the finite element approximation on the Reduced Basis error. We propose an adaptive algorithm, based on the a posteriori Reduced Basis error estimate, for the selection of the sample sets upon which the basis are built; the idea leading this algorithm is the minimization of the computational costs associated with the solution of the Reduced Basis problem. Numerical tests demonstrate the efficiency, in terms of computational costs, of the ＂primal-dual＂ Reduced Basis approach with respect to an ＂only primal＂ one. Parametrized advection-reaction partial differential equations, Reduced Basis method, ＂primal-dual＂ reduced basis approach, Stabilized finite element method, a posteriori error estimation.
文摘Based on a new DIY concept for software development, an automatic program-generating technology attached on a software system called as Finite Element Program Generator （FEPG） provides a platform of developing programs, through which a scientific researcher can submit his special physico-mathematical problem to the system in a more direct and convenient way for solution. For solving flow and heat problems by using finite element method, the stabilization technologies and fraction-step methods are adopted to overcome the numerical difficul- ties caused mainly due to the dominated convection. A couple of benchmark problems are given in this paper as examples to illustrate the usage and the superiority of the automatic program generation technique, including the flow in a lid-driven cavity, the starting flow in a circular pipe, the natural convection in a square cavity, and the flow past a circular cylinder, etc. They are also shown as the verification of the algorithms.
