In this paper,a linearized energy stable numerical scheme is used to solve the modified Cahn-Hilliard-Navier-Stokes model,which is a phase-field model for two-phase incompressible flows.The time discretization is base...In this paper,a linearized energy stable numerical scheme is used to solve the modified Cahn-Hilliard-Navier-Stokes model,which is a phase-field model for two-phase incompressible flows.The time discretization is based on the convex splitting of the energy functional,which leads to a linearized system.In order to maintain the energy stability,the definition domain of energy function is extended to infinity.The stability of the scheme is proved and the error estimate is given.Numerical experiments are done to demonstrate the effectiveness for the proposed scheme.展开更多
In this paper, we propose a dimensional splitting method for the three dimensional （3D） rotating Navier-Stokes equations. Assume that the domain is a channel bounded by two surfaces and is decomposed by a series of...In this paper, we propose a dimensional splitting method for the three dimensional （3D） rotating Navier-Stokes equations. Assume that the domain is a channel bounded by two surfaces and is decomposed by a series of surfaces i into several sub-domains, which are called the layers of the flow. Every interface i between two sub-domains shares the same geometry. After establishing a semi-geodesic coordinate （S-coordinate） system based on i, Navier-Stoke equations in this coordinate can be expressed as the sum of two operators, of which one is called the membrane operator defined on the tangent space on i, another one is called the bending operator taking value in the normal space on i. Then the derivatives of velocity with respect to the normal direction of the surface are approximated by the Euler central difference, and an approximate form of Navier-Stokes equations on the surface i is obtained, which is called the two-dimensional three-component （2D-3C） Navier-Stokes equations on a two dimensional manifold. Solving these equations by alternate iteration, an approximate solution to the original 3D Navier-Stokes equations is obtained. In addition, the proof of the existence of solutions to 2D-3C Navier-Stokes equations is provided, and some approximate methods for solving 2D-3C Navier-Stot4es equations are presented.展开更多
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 this paper, for a semi-linear parabolic partial differential equations with impulsive effects, the existence-comparison theorem and comparison principles are established using the method of upper and lower solution...In this paper, for a semi-linear parabolic partial differential equations with impulsive effects, the existence-comparison theorem and comparison principles are established using the method of upper and lower solutions. These results are applied to obtain the stability results of the steady-state solutions in a reaction-diffusion equations modelling two competing species with instantaneous stocking.展开更多
In this paper we represent a new numerical method for solving the steady Navier-Stokes equations in three dimensional unbounded domain. The method consists in coupling the boundary integral and the finite element nonl...In this paper we represent a new numerical method for solving the steady Navier-Stokes equations in three dimensional unbounded domain. The method consists in coupling the boundary integral and the finite element nonlinear Galerkin methods. An artificial smooth boundary is introduced seperating an interior inhomogeneous region from an exterior one. The Navier-Stokes equations in the exterior region are approximated by the Oseen equations and the approximate solution is represented by an integral equation over the artificial boundary. Moreover, a finite element nonlinear Galerkin method is used to approximate the resulting variational problem. Finally, the existence and error estimates are derived.展开更多
In this paper, the fundamental solution of rotating generalized Stokes problem in R^3 is established. To obtain it, some fundamental solutions of other problems also are established, such as generalized Laplace proble...In this paper, the fundamental solution of rotating generalized Stokes problem in R^3 is established. To obtain it, some fundamental solutions of other problems also are established, such as generalized Laplace problem, generalized Stokes problem and rotating Stokes problem.展开更多
The Navier-Stokes-α equations subject to the periodic boundary conditions are considered. Analyticity in time for a class of solutions taking values in a Gevrey class of functions is proven. Exponential decay of the ...The Navier-Stokes-α equations subject to the periodic boundary conditions are considered. Analyticity in time for a class of solutions taking values in a Gevrey class of functions is proven. Exponential decay of the spatial Fourier spectrum for the analytic solutions and the lower bounds on the rate defined by the exponential decay are also obtained.展开更多
This paper deals with the boundary integral method to study the Navier-Stokes equations around a rotating obstacle. The detail of this method is that the exterior domain is truncated into a bounded domain and a new ex...This paper deals with the boundary integral method to study the Navier-Stokes equations around a rotating obstacle. The detail of this method is that the exterior domain is truncated into a bounded domain and a new exterior domain by introducing some open ball BR, and the nonlinear problem in the bounded domain and the linearized problem in the new exterior domain are considered and the approximation coupled problem is obtained. We show that the error between the solution u of Navier-Stokes equations around a rotating obstacle and the solution ue of the approximation coupled problem is O（R-1/4） in the Hl-seminorm when Iwl does not exceed some constant.展开更多
基金Supported by the Provincial Natural Science Foundation of Shanxi(No.201901D111123)Key Research and Development(R&D)Projects of Shanxi Province(No.201903D121038)。
文摘In this paper,a linearized energy stable numerical scheme is used to solve the modified Cahn-Hilliard-Navier-Stokes model,which is a phase-field model for two-phase incompressible flows.The time discretization is based on the convex splitting of the energy functional,which leads to a linearized system.In order to maintain the energy stability,the definition domain of energy function is extended to infinity.The stability of the scheme is proved and the error estimate is given.Numerical experiments are done to demonstrate the effectiveness for the proposed scheme.
基金Supported by the National High-Tech Research and Development Program of China (No. 2009AA01A135)the National Natural Science Foundation of China (Nos. 10971165, 11001216, 11071193, 10871156)the Foundation of AVIC Chengdu Aircraft Design and Research Institute
文摘In this paper, we propose a dimensional splitting method for the three dimensional （3D） rotating Navier-Stokes equations. Assume that the domain is a channel bounded by two surfaces and is decomposed by a series of surfaces i into several sub-domains, which are called the layers of the flow. Every interface i between two sub-domains shares the same geometry. After establishing a semi-geodesic coordinate （S-coordinate） system based on i, Navier-Stoke equations in this coordinate can be expressed as the sum of two operators, of which one is called the membrane operator defined on the tangent space on i, another one is called the bending operator taking value in the normal space on i. Then the derivatives of velocity with respect to the normal direction of the surface are approximated by the Euler central difference, and an approximate form of Navier-Stokes equations on the surface i is obtained, which is called the two-dimensional three-component （2D-3C） Navier-Stokes equations on a two dimensional manifold. Solving these equations by alternate iteration, an approximate solution to the original 3D Navier-Stokes equations is obtained. In addition, the proof of the existence of solutions to 2D-3C Navier-Stokes equations is provided, and some approximate methods for solving 2D-3C Navier-Stot4es equations are presented.
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Supported by the National Natural Science Foundation of China(No.10071048).
文摘In this paper, for a semi-linear parabolic partial differential equations with impulsive effects, the existence-comparison theorem and comparison principles are established using the method of upper and lower solutions. These results are applied to obtain the stability results of the steady-state solutions in a reaction-diffusion equations modelling two competing species with instantaneous stocking.
文摘In this paper we represent a new numerical method for solving the steady Navier-Stokes equations in three dimensional unbounded domain. The method consists in coupling the boundary integral and the finite element nonlinear Galerkin methods. An artificial smooth boundary is introduced seperating an interior inhomogeneous region from an exterior one. The Navier-Stokes equations in the exterior region are approximated by the Oseen equations and the approximate solution is represented by an integral equation over the artificial boundary. Moreover, a finite element nonlinear Galerkin method is used to approximate the resulting variational problem. Finally, the existence and error estimates are derived.
基金Supported by the National Natural Science Foundation of China (No. 10571142)
文摘In this paper, the fundamental solution of rotating generalized Stokes problem in R^3 is established. To obtain it, some fundamental solutions of other problems also are established, such as generalized Laplace problem, generalized Stokes problem and rotating Stokes problem.
文摘The Navier-Stokes-α equations subject to the periodic boundary conditions are considered. Analyticity in time for a class of solutions taking values in a Gevrey class of functions is proven. Exponential decay of the spatial Fourier spectrum for the analytic solutions and the lower bounds on the rate defined by the exponential decay are also obtained.
基金the National Natural Science Foundation of China(No.10901122,No.11001205)Zhejiang Provincial Natural Science Foundation of China(No.LY12A01015)
文摘This paper deals with the boundary integral method to study the Navier-Stokes equations around a rotating obstacle. The detail of this method is that the exterior domain is truncated into a bounded domain and a new exterior domain by introducing some open ball BR, and the nonlinear problem in the bounded domain and the linearized problem in the new exterior domain are considered and the approximation coupled problem is obtained. We show that the error between the solution u of Navier-Stokes equations around a rotating obstacle and the solution ue of the approximation coupled problem is O（R-1/4） in the Hl-seminorm when Iwl does not exceed some constant.
