In this paper, we study the evolution of hypersurface moving by the mean curvature minus an external force field. It is shown that the flow will blow up in a finite time if the mean curvature of the initial surface is...In this paper, we study the evolution of hypersurface moving by the mean curvature minus an external force field. It is shown that the flow will blow up in a finite time if the mean curvature of the initial surface is larger than some constant depending on the boundness of derivatives of the external force field. For a linear force, we prove that the convexity of the hypersurface is preserved during the evolution and the flow has a unique smooth solution in any finite time and expands to infinity as the time tends to infinity if the initial curvature is smaller than the slope of the force.展开更多
A new coupled finite element formulation is proposed to calculate a conformation tensor model in two complex flows： a planar contraction flow and a planar flow around a symmetrically placed cylinder. The components o...A new coupled finite element formulation is proposed to calculate a conformation tensor model in two complex flows： a planar contraction flow and a planar flow around a symmetrically placed cylinder. The components of conformation tensor are first computed together with the velocity and pressure to describe the change of morphology of polymer chain coils in flow fields. Macroscopic quantities of viscoelastic flow are then calculated based on the conformation tensor. Comparisons between the numerical simulations and experiments for stress patterns and velocity profiles are carried out to prove the validity of the method.展开更多
Numerical simulation of two-phase flow in fractured karst reservoirs is still a challenging issue.The triple-porosity model is the major approach up to now.However,the triple-continuum assumption in this model is unac...Numerical simulation of two-phase flow in fractured karst reservoirs is still a challenging issue.The triple-porosity model is the major approach up to now.However,the triple-continuum assumption in this model is unacceptable for many cases.In the present work,an efficient numerical model has been developed for immiscible two-phase flowin fractured karst reservoirs based on the idea of equivalent continuum representation.First,based on the discrete fracture-vug model and homogenization theory,the effective absolute permeability tensors for each grid blocks are calculated.And then an analytical procedure to obtain a pseudo relative permeability curves for a grid block containing fractures and cavities has been successfully implemented.Next,a full-tensor simulator has been designed based on a hybrid numerical method(combining mixed finite element method and finite volume method).A simple fracture system has been used to demonstrate the validity of our method.At last,we have used the fracture and cavity statistics data fromTAHE outcrops in west China,effective permeability values and other parameters from our code,and an equivalent continuum simulator to calculate the water flooding profiles for more realistic systems.展开更多
In this article, we study the steady, shrinking, and expanding Kahler-Ricci solitons with vanishing Bochner-Weyl tensor and prove that, under this condition, the Ricci solitons must have constant holomorphic sectional...In this article, we study the steady, shrinking, and expanding Kahler-Ricci solitons with vanishing Bochner-Weyl tensor and prove that, under this condition, the Ricci solitons must have constant holomorphic sectional curvature.展开更多
On the basis of the vector formula of the Newton’s law for a viscous liquid and the integrated vector form of the equation of an impulse for a viscous liquid for resistance and carrying power of a profile of any form...On the basis of the vector formula of the Newton’s law for a viscous liquid and the integrated vector form of the equation of an impulse for a viscous liquid for resistance and carrying power of a profile of any form and the big length dependences are found in a stream. Application of the found dependences at a circulating flow of the cylinder located across a stream is showed. The analysis of a tensor of viscosity for laminar and turbulent flow is carried out.展开更多
In this paper, we study the complete bounded λ-hypersurfaces in the weighted volume-preserving mean curvature flow. Firstly, we investigate the volume comparison theorem of complete bounded λ-hypersurfaces with |A|...In this paper, we study the complete bounded λ-hypersurfaces in the weighted volume-preserving mean curvature flow. Firstly, we investigate the volume comparison theorem of complete bounded λ-hypersurfaces with |A|≤α and get some applications of the volume comparison theorem. Secondly, we consider the relation among λ, extrinsic radius k, intrinsic diameter d, and dimension n of the complete λ-hypersurface,and we obtain some estimates for the intrinsic diameter and the extrinsic radius. At last, we get some topological properties of the bounded λ-hypersurface with some natural and general restrictions.展开更多
The effect of pre-shear flow on the subsequent crystallization process of polymeric melt was investigated and a flow-induced crystallization （FIC） model based on the conformation tensor incorporating the pre-shear e...The effect of pre-shear flow on the subsequent crystallization process of polymeric melt was investigated and a flow-induced crystallization （FIC） model based on the conformation tensor incorporating the pre-shear effect was proposed. The model is capable of predicting the overshoot phenomena of the stress and the flow-induced free energy change of the polymeric system at high pre-shear rates. Under the condition of flow, the increase in the activated nuclei number was contributed by the flow-induced free energy change, which showed an overwhelming effect on the nuclei formation during the pre-shear process at high shear rates. The half crystallization time （t1/2） of polypropylene （PP） as functions of pre-shear rate and pre-shear time at different crystallization temperatures was predicted and compared with the experiment data. Both numerical and experimental results showed that t1/2 of PP decreased dramatically when the flow started but leveled off at long times. It was found that two transformation stages in t1/2 existed within a wide range of shear rates. For the first stage where the melting polymer experienced a relatively weak shear flow, the acceleration of crystallization kinetics was mainly contributed by the steady value of free energy change while in the second stage for high shear rates, strong overshoot in flow-induced free energy change occurred and the crystallization kinetics was thus significantly enhanced. The overshoots in stress and flow-induced free energy change reflected an important role of flow on the primary nucleation especially when the flow was strong enough.展开更多
A new continuum theory of the constitutive equation of co-rotational derivative type is developed for anisotropic viscoelastic fluid—liquid crystalline (LC) polymers. A new concept of simple anisotropic fluid is intr...A new continuum theory of the constitutive equation of co-rotational derivative type is developed for anisotropic viscoelastic fluid—liquid crystalline (LC) polymers. A new concept of simple anisotropic fluid is introduced. On the basis of principles of anisotropic simple fluid, stress behaviour is described by velocity gradient tensor and spin tensor instead of the velocity gradient tensor in the classic Leslie—Ericksen continuum theory. Analyzing rheological nature of the fluid and using tensor analysis a general form of the constitutive equ- ation of co-rotational type is established for the fluid. A special term of high order in the equation is introduced by author to describe the sp- ecial change of the normal stress differences which is considered as a result of director tumbling by Larson et al. Analyzing the experimental results by Larson et al., a principle of Non- oscillatory normal stress is introduced which leads to simplification of the problem with relaxation times. The special behaviour of non- symmetry of the shear stress is predicted by using the present model for LC polymer liquids. Two shear stresses in shear flow of LC polymer liquids may lead to vortex and rotation flow, i.e. director tumbling in the flow. The first and second normal stress differences are calculated by the model special behaviour of which is in agree- ment with experiments. In the research, the com- putational symbolic manipulation such as computer software Maple is used. For the anisotropic viscoelastic fluid the constitutive equation theory is of important fundamental significance.展开更多
In this paper we consider mixed finite element methods for second order elliptic problems. In the case of the lowest order Brezzi-Douglas-Marini elements （if d = 2） or Brezzi- Douglas-Duran-Fortin elements （if d = ...In this paper we consider mixed finite element methods for second order elliptic problems. In the case of the lowest order Brezzi-Douglas-Marini elements （if d = 2） or Brezzi- Douglas-Duran-Fortin elements （if d = 3） on rectangular parallelepipeds, we show that the mixed method system, by incorporating certain quadrature rules, can be written as a simple, cell-centered finite difference method. This leads to the solution of a sparse, positive semidefinite linear system for the scalar unknown. For a diagonal tensor coefficient, the sparsity pattern for the scalar unknown is a five point stencil if d = 2, and seven if d = 3. For a general tensor coefficient, it is a nine point stencil, and nineteen, respectively. Applications of the mixed method implementation as finite differences to nonisothermal multiphase, multicomponent flow in porous media are presented.展开更多
基金This work was partially supported by the National Natural Science Foundation of China (Grant No. 10631020)Basic Research Grant of Tsinghua University (Grant No. JCJC2005071).
文摘In this paper, we study the evolution of hypersurface moving by the mean curvature minus an external force field. It is shown that the flow will blow up in a finite time if the mean curvature of the initial surface is larger than some constant depending on the boundness of derivatives of the external force field. For a linear force, we prove that the convexity of the hypersurface is preserved during the evolution and the flow has a unique smooth solution in any finite time and expands to infinity as the time tends to infinity if the initial curvature is smaller than the slope of the force.
基金This work was financially supported by the National Natural Science Foundation of China(Nos.20204007 and 50390090)the Doctoral Foundation of National Education Committee of China(No.20030248008)the 863 Project of China(No.2002AA336120).
文摘A new coupled finite element formulation is proposed to calculate a conformation tensor model in two complex flows： a planar contraction flow and a planar flow around a symmetrically placed cylinder. The components of conformation tensor are first computed together with the velocity and pressure to describe the change of morphology of polymer chain coils in flow fields. Macroscopic quantities of viscoelastic flow are then calculated based on the conformation tensor. Comparisons between the numerical simulations and experiments for stress patterns and velocity profiles are carried out to prove the validity of the method.
基金supported by the National Basic Research Program of China(“973”Program)(Grant No.2011CB201004)the ImportantNational Science and Technology Project of China(Grant No.2011ZX05014-005-003HZ)+2 种基金the National Natural Science Foundation of China(Grant No.11102237)the Introducing Talents of Discipline to Universities of China(Grant No.B08028)the Fundamental Research Funds for the Central Universities(Grant No.27R1102065A).
文摘Numerical simulation of two-phase flow in fractured karst reservoirs is still a challenging issue.The triple-porosity model is the major approach up to now.However,the triple-continuum assumption in this model is unacceptable for many cases.In the present work,an efficient numerical model has been developed for immiscible two-phase flowin fractured karst reservoirs based on the idea of equivalent continuum representation.First,based on the discrete fracture-vug model and homogenization theory,the effective absolute permeability tensors for each grid blocks are calculated.And then an analytical procedure to obtain a pseudo relative permeability curves for a grid block containing fractures and cavities has been successfully implemented.Next,a full-tensor simulator has been designed based on a hybrid numerical method(combining mixed finite element method and finite volume method).A simple fracture system has been used to demonstrate the validity of our method.At last,we have used the fracture and cavity statistics data fromTAHE outcrops in west China,effective permeability values and other parameters from our code,and an equivalent continuum simulator to calculate the water flooding profiles for more realistic systems.
基金supported by the National Natural Science Foundation of China under the grant numbers 11126073the Fundamental Research Funds for the Central Universities of SCUT under the grant number 2012ZB0017
文摘In this article, we study the steady, shrinking, and expanding Kahler-Ricci solitons with vanishing Bochner-Weyl tensor and prove that, under this condition, the Ricci solitons must have constant holomorphic sectional curvature.
文摘On the basis of the vector formula of the Newton’s law for a viscous liquid and the integrated vector form of the equation of an impulse for a viscous liquid for resistance and carrying power of a profile of any form and the big length dependences are found in a stream. Application of the found dependences at a circulating flow of the cylinder located across a stream is showed. The analysis of a tensor of viscosity for laminar and turbulent flow is carried out.
基金supported by National Natural Science Foundation of China (Grant No. 11271343)
文摘In this paper, we study the complete bounded λ-hypersurfaces in the weighted volume-preserving mean curvature flow. Firstly, we investigate the volume comparison theorem of complete bounded λ-hypersurfaces with |A|≤α and get some applications of the volume comparison theorem. Secondly, we consider the relation among λ, extrinsic radius k, intrinsic diameter d, and dimension n of the complete λ-hypersurface,and we obtain some estimates for the intrinsic diameter and the extrinsic radius. At last, we get some topological properties of the bounded λ-hypersurface with some natural and general restrictions.
基金supported by the National Natural Science Foundation of China(No.10590355)the Shanghai Leading Academic Discipline Project(No.B202)
文摘The effect of pre-shear flow on the subsequent crystallization process of polymeric melt was investigated and a flow-induced crystallization （FIC） model based on the conformation tensor incorporating the pre-shear effect was proposed. The model is capable of predicting the overshoot phenomena of the stress and the flow-induced free energy change of the polymeric system at high pre-shear rates. Under the condition of flow, the increase in the activated nuclei number was contributed by the flow-induced free energy change, which showed an overwhelming effect on the nuclei formation during the pre-shear process at high shear rates. The half crystallization time （t1/2） of polypropylene （PP） as functions of pre-shear rate and pre-shear time at different crystallization temperatures was predicted and compared with the experiment data. Both numerical and experimental results showed that t1/2 of PP decreased dramatically when the flow started but leveled off at long times. It was found that two transformation stages in t1/2 existed within a wide range of shear rates. For the first stage where the melting polymer experienced a relatively weak shear flow, the acceleration of crystallization kinetics was mainly contributed by the steady value of free energy change while in the second stage for high shear rates, strong overshoot in flow-induced free energy change occurred and the crystallization kinetics was thus significantly enhanced. The overshoots in stress and flow-induced free energy change reflected an important role of flow on the primary nucleation especially when the flow was strong enough.
文摘A new continuum theory of the constitutive equation of co-rotational derivative type is developed for anisotropic viscoelastic fluid—liquid crystalline (LC) polymers. A new concept of simple anisotropic fluid is introduced. On the basis of principles of anisotropic simple fluid, stress behaviour is described by velocity gradient tensor and spin tensor instead of the velocity gradient tensor in the classic Leslie—Ericksen continuum theory. Analyzing rheological nature of the fluid and using tensor analysis a general form of the constitutive equ- ation of co-rotational type is established for the fluid. A special term of high order in the equation is introduced by author to describe the sp- ecial change of the normal stress differences which is considered as a result of director tumbling by Larson et al. Analyzing the experimental results by Larson et al., a principle of Non- oscillatory normal stress is introduced which leads to simplification of the problem with relaxation times. The special behaviour of non- symmetry of the shear stress is predicted by using the present model for LC polymer liquids. Two shear stresses in shear flow of LC polymer liquids may lead to vortex and rotation flow, i.e. director tumbling in the flow. The first and second normal stress differences are calculated by the model special behaviour of which is in agree- ment with experiments. In the research, the com- putational symbolic manipulation such as computer software Maple is used. For the anisotropic viscoelastic fluid the constitutive equation theory is of important fundamental significance.
文摘In this paper we consider mixed finite element methods for second order elliptic problems. In the case of the lowest order Brezzi-Douglas-Marini elements （if d = 2） or Brezzi- Douglas-Duran-Fortin elements （if d = 3） on rectangular parallelepipeds, we show that the mixed method system, by incorporating certain quadrature rules, can be written as a simple, cell-centered finite difference method. This leads to the solution of a sparse, positive semidefinite linear system for the scalar unknown. For a diagonal tensor coefficient, the sparsity pattern for the scalar unknown is a five point stencil if d = 2, and seven if d = 3. For a general tensor coefficient, it is a nine point stencil, and nineteen, respectively. Applications of the mixed method implementation as finite differences to nonisothermal multiphase, multicomponent flow in porous media are presented.
