In this paper,a streamline diffusion F.E.M. for linear Sobolev equations with convection dominated term is given.According to the range of space time F.E mesh parameter h ,two choices for artifical diffusion par...In this paper,a streamline diffusion F.E.M. for linear Sobolev equations with convection dominated term is given.According to the range of space time F.E mesh parameter h ,two choices for artifical diffusion parameter δ are presented,and for the corresponding computation schemes the stability and error estimates in suitable norms are estabilished.展开更多
In this paper,ETD3-Padéand ETD4-PadéGalerkin finite element methods are proposed and analyzed for nonlinear delayed convection-diffusion-reaction equations with Dirichlet boundary conditions.An ETD-based RK ...In this paper,ETD3-Padéand ETD4-PadéGalerkin finite element methods are proposed and analyzed for nonlinear delayed convection-diffusion-reaction equations with Dirichlet boundary conditions.An ETD-based RK is used for time integration of the corresponding equation.To overcome a well-known difficulty of numerical instability associated with the computation of the exponential operator,the Padéapproach is used for such an exponential operator approximation,which in turn leads to the corresponding ETD-Padéschemes.An unconditional L^(2) numerical stability is proved for the proposed numerical schemes,under a global Lipshitz continuity assumption.In addition,optimal rate error estimates are provided,which gives the convergence order of O(k^(3)+h^(r))(ETD3-Padé)or O(k^(4)+h^(r))(ETD4-Padé)in the L^(2)norm,respectively.Numerical experiments are presented to demonstrate the robustness of the proposed numerical schemes.展开更多
We investigate the linearization of systems of n-component nonlinear diffusion equations; such systems have physical applications in soil science, mathematical biology and invariant curve flows. Equivalence transforma...We investigate the linearization of systems of n-component nonlinear diffusion equations; such systems have physical applications in soil science, mathematical biology and invariant curve flows. Equivalence transformations of their auxiliary systems are used to identify the systems that can be linearized. We also provide several examples of systems with two-component equations, and show how to linearize them by nonlocal mappings.展开更多
This paper is concerned with the mutual effects of viscous dissipation and slip effects on a rotating vertical cone in a viscous fluid. Similarity solutions for rotating cone with wall temperature boundary conditions ...This paper is concerned with the mutual effects of viscous dissipation and slip effects on a rotating vertical cone in a viscous fluid. Similarity solutions for rotating cone with wall temperature boundary conditions provides a system of nonlinear ordinary differential equations which have been treated by optimal homotopy analysis method（OHAM）. The obtained analytical results in comparison with the numerical ones show a noteworthy accuracy for a special case. Effects for the velocities and temperature are revealed graphically and the tabulated values of the surface shear stresses and the heat transfer rate are entered in tables. From the study it is seen that the slip parameter γ enhances the primary velocity while the secondary velocity reduces. Further it is observed that the heat transfer rate Nu Re-1/2x increases with Eckert number Ec and Prandtl number Pr.展开更多
We propose a mass-conservative and monotonicity-preserving characteristic finite element method for solving three-dimensional transport and incompressibleNavier-Stokes equations on unstructured grids. The main idea i...We propose a mass-conservative and monotonicity-preserving characteristic finite element method for solving three-dimensional transport and incompressibleNavier-Stokes equations on unstructured grids. The main idea in the proposed algorithm consists of combining a mass-conservative and monotonicity-preserving modified method of characteristics for the time integration with a mixed finite elementmethod for the space discretization. This class of computational solvers benefits fromthe geometrical flexibility of the finite elements and the strong stability of the modi-fied method of characteristics to accurately solve convection-dominated flows usingtime steps larger than its Eulerian counterparts. In the current study, we implementthree-dimensional limiters to convert the proposed solver to a fully mass-conservativeand essentially monotonicity-preserving method in addition of a low computationalcost. The key idea lies on using quadratic and linear basis functions of the mesh element where the departure point is localized in the interpolation procedures. Theproposed method is applied to well-established problems for transport and incompressible Navier-Stokes equations in three space dimensions. The numerical resultsillustrate the performance of the proposed solver and support its ability to yield accurate and efficient numerical solutions for three-dimensional convection-dominatedflow problems on unstructured tetrahedral meshes.展开更多
A two-grid method for solving nonlinear convection-dominated diffusion equations is presented. The method use discretizations based on a characteristic mixed finite-element method and give the linearization for nonlin...A two-grid method for solving nonlinear convection-dominated diffusion equations is presented. The method use discretizations based on a characteristic mixed finite-element method and give the linearization for nonlinear systems by two steps. The error analysis shows that the two-grid scheme combined with the characteristic mixed finite-element method can decrease numerical oscillation caused by dominated convections and solve nonlinear advection-dominated diffusion problems efficiently.展开更多
We perform a comparison in terms of accuracy and CPU time between second order BDF semi-Lagrangian and Lagrange-Galerkin schemes in combination with high order finite element method.The numerical results show that for...We perform a comparison in terms of accuracy and CPU time between second order BDF semi-Lagrangian and Lagrange-Galerkin schemes in combination with high order finite element method.The numerical results show that for polynomials of degree 2 semi-Lagrangian schemes are faster than Lagrange-Galerkin schemes for the same number of degrees of freedom,however,for the same level of accuracy both methods are about the same in terms of CPU time.For polynomials of degree larger than 2,Lagrange-Galerkin schemes behave better than semi-Lagrangian schemes in terms of both accuracy and CPU time;specially,for polynomials of degree 8 or larger.Also,we have performed tests on the parallelization of these schemes and the speedup obtained is quasi-optimal even with more than 100 processors.展开更多
In this article,a Crank-Nicolson/Explicit scheme is designed and analyzed for the time-dependent natural convection problem with nonsmooth initial data.The Galerkin finite element method(FEM)with stable MINI element i...In this article,a Crank-Nicolson/Explicit scheme is designed and analyzed for the time-dependent natural convection problem with nonsmooth initial data.The Galerkin finite element method(FEM)with stable MINI element is used for the velocity and pressure and linear polynomial for the temperature.The time discretization is based on the Crank-Nicolson scheme.In order to simplify the computations,the nonlinear terms are treated by the explicit scheme.The advantages of our numerical scheme can be list as follows:(1)The original problem is split into two linear subproblems,these subproblems can be solved in each time level in parallel and the computational sizes are smaller than the origin one.(2)A constant coefficient linear discrete algebraic system is obtained in each subproblem and the computation becomes easy.The main contributions of this work are the stability and convergence results of numerical solutions with nonsmooth initial data.Finally,some numerical results are presented to verify the established theoretical results and show the performances of the developed numerical scheme.展开更多
This paper is concerned with a stabilized finite element method based on two local Gauss integrations for the two-dimensional non-stationary conductionconvection equations by using the lowest equal-order pairs of fin...This paper is concerned with a stabilized finite element method based on two local Gauss integrations for the two-dimensional non-stationary conductionconvection equations by using the lowest equal-order pairs of finite elements.This method only offsets the discrete pressure space by the residual of the simple and symmetry term at element level in order to circumvent the inf-sup condition.The stability of the discrete scheme is derived under some regularity assumptions.Optimal error estimates are obtained by applying the standard Galerkin techniques.Finally,the numerical illustrations agree completely with the theoretical expectations.展开更多
We develop a new sixth-order accurate numerical scheme for the solution of two point boundary value problems.The scheme uses nonpolynomial spline basis and high order finite difference approximations.With the help of ...We develop a new sixth-order accurate numerical scheme for the solution of two point boundary value problems.The scheme uses nonpolynomial spline basis and high order finite difference approximations.With the help of spline functions,we derive consistency conditions and it is used to derive high order discretizations of the first derivative.The resulting difference schemes are solved by the standard Newton’s method and have very small computing time.The new method is analyzed for its convergence and the efficiency of the proposed scheme is illustrated by convection-diffusion problem and nonlinear Lotka–Volterra equation.The order of convergence and maximum absolute errors are computed to present the utility of the new scheme.展开更多
This study is focused on a steady dissipative layer, which is generated by Marangoni convection flow over the surface resulted from an imposed temperature gradient, coupled with buoyancy effects due to gravity and ext...This study is focused on a steady dissipative layer, which is generated by Marangoni convection flow over the surface resulted from an imposed temperature gradient, coupled with buoyancy effects due to gravity and external pressure. A model is proposed with Marangoni condition in the boundary conditions at the interface. The similarity equations are determined and approximate analytical solutions are obtained by an efficient transformation, asymptotic expansion and Pade approximant technique. For the cases that buoyancy force is favorable or unfavor-able to Marangoni flow, the features of flow and temperature fields are investigated in terms of Marangoni mixed convection parameter and Prantl number.展开更多
Hot air producing is one of the most important engineering applications in recent years.It is a technique used in various thermodynamic systems,such as home heating systems,food dryers.One of the main problems impedin...Hot air producing is one of the most important engineering applications in recent years.It is a technique used in various thermodynamic systems,such as home heating systems,food dryers.One of the main problems impeding the spread of hot air producing technology is the lack of homogeneity of the heat flow coming from hot air generators as well as an inadequate flow rate.The most of the existing hot air generators require to be supported by systems that can increase the low volumetric flow and the air temperature of these generators,through increasing the speed of the flow of air emitted or lifting the drawer Heat,which contributes to raising the overall cost.However,to improve the thermal and dynamic quality of the hot air flow produced by the generator,a numerical investigation of the free convection flow inside two different configurations is presented in this thesis.The primary objective of this work is to predict the behavior of the flow inside tow configurations,the first one consists of a vertical cylinder with heated walls,and the second configuration is an open-ended vertical cylinder with a hot disc placed at the entrance(configuration A,configuration B).This work characterizes through the examination of this flow,the variables that control an air emission with high flow rate and a high and homogeneous temperature to represent the appropriate criteria that should be respected to obtain a hot air generator overcoming the previously mentioned constraints.Furthermore;the results of this work show the influence the boundary conditions and Rayleigh number on the resulting flow.展开更多
It is well-known that physical laws for large chaotic dynamical systems are revealed statistically.Many times these statistical properties of the system must be approximated numerically.The main contribution of this m...It is well-known that physical laws for large chaotic dynamical systems are revealed statistically.Many times these statistical properties of the system must be approximated numerically.The main contribution of this manuscript is to provide simple and natural criterions on numerical methods (temporal and spatial discretization) that are able to capture the stationary statistical properties of the underlying dissipative chaotic dynamical systems asymptotically.The result on temporal approximation is a recent finding of the author,and the result on spatial approximation is a new one.Applications to the infinite Prandtl number model for convection and the barotropic quasi-geostrophic model are also discussed.展开更多
In this paper,we investigate a stochastic meshfree finite volume element method for an optimal control problem governed by the convection diffusion equations with random coefficients.There are two contributions of thi...In this paper,we investigate a stochastic meshfree finite volume element method for an optimal control problem governed by the convection diffusion equations with random coefficients.There are two contributions of this paper.Firstly,we establish a scheme to approximate the optimality system by using the finite volume element method in the physical space and the meshfree method in the probability space,which is competitive for high-dimensional random inputs.Secondly,the a priori error estimates are derived for the state,the co-state and the control variables.Some numerical tests are carried out to confirm the theoretical results and demonstrate the efficiency of the proposed method.展开更多
基金Supported by the National Natural Sciences Foundation of China(1 8971 0 51 )
文摘In this paper,a streamline diffusion F.E.M. for linear Sobolev equations with convection dominated term is given.According to the range of space time F.E mesh parameter h ,two choices for artifical diffusion parameter δ are presented,and for the corresponding computation schemes the stability and error estimates in suitable norms are estabilished.
文摘In this paper,ETD3-Padéand ETD4-PadéGalerkin finite element methods are proposed and analyzed for nonlinear delayed convection-diffusion-reaction equations with Dirichlet boundary conditions.An ETD-based RK is used for time integration of the corresponding equation.To overcome a well-known difficulty of numerical instability associated with the computation of the exponential operator,the Padéapproach is used for such an exponential operator approximation,which in turn leads to the corresponding ETD-Padéschemes.An unconditional L^(2) numerical stability is proved for the proposed numerical schemes,under a global Lipshitz continuity assumption.In addition,optimal rate error estimates are provided,which gives the convergence order of O(k^(3)+h^(r))(ETD3-Padé)or O(k^(4)+h^(r))(ETD4-Padé)in the L^(2)norm,respectively.Numerical experiments are presented to demonstrate the robustness of the proposed numerical schemes.
基金Supported by the National Natural Science Foundation of China under Grant No 10671156, and the Programme for New Century Excellent Talents in University （NCET-04-0968）.
文摘We investigate the linearization of systems of n-component nonlinear diffusion equations; such systems have physical applications in soil science, mathematical biology and invariant curve flows. Equivalence transformations of their auxiliary systems are used to identify the systems that can be linearized. We also provide several examples of systems with two-component equations, and show how to linearize them by nonlocal mappings.
文摘This paper is concerned with the mutual effects of viscous dissipation and slip effects on a rotating vertical cone in a viscous fluid. Similarity solutions for rotating cone with wall temperature boundary conditions provides a system of nonlinear ordinary differential equations which have been treated by optimal homotopy analysis method（OHAM）. The obtained analytical results in comparison with the numerical ones show a noteworthy accuracy for a special case. Effects for the velocities and temperature are revealed graphically and the tabulated values of the surface shear stresses and the heat transfer rate are entered in tables. From the study it is seen that the slip parameter γ enhances the primary velocity while the secondary velocity reduces. Further it is observed that the heat transfer rate Nu Re-1/2x increases with Eckert number Ec and Prandtl number Pr.
文摘We propose a mass-conservative and monotonicity-preserving characteristic finite element method for solving three-dimensional transport and incompressibleNavier-Stokes equations on unstructured grids. The main idea in the proposed algorithm consists of combining a mass-conservative and monotonicity-preserving modified method of characteristics for the time integration with a mixed finite elementmethod for the space discretization. This class of computational solvers benefits fromthe geometrical flexibility of the finite elements and the strong stability of the modi-fied method of characteristics to accurately solve convection-dominated flows usingtime steps larger than its Eulerian counterparts. In the current study, we implementthree-dimensional limiters to convert the proposed solver to a fully mass-conservativeand essentially monotonicity-preserving method in addition of a low computationalcost. The key idea lies on using quadratic and linear basis functions of the mesh element where the departure point is localized in the interpolation procedures. Theproposed method is applied to well-established problems for transport and incompressible Navier-Stokes equations in three space dimensions. The numerical resultsillustrate the performance of the proposed solver and support its ability to yield accurate and efficient numerical solutions for three-dimensional convection-dominatedflow problems on unstructured tetrahedral meshes.
文摘A two-grid method for solving nonlinear convection-dominated diffusion equations is presented. The method use discretizations based on a characteristic mixed finite-element method and give the linearization for nonlinear systems by two steps. The error analysis shows that the two-grid scheme combined with the characteristic mixed finite-element method can decrease numerical oscillation caused by dominated convections and solve nonlinear advection-dominated diffusion problems efficiently.
基金funded by grant CGL2007-66440-C04-01 from Ministerio de Educacion y Ciencia de Espana.
文摘We perform a comparison in terms of accuracy and CPU time between second order BDF semi-Lagrangian and Lagrange-Galerkin schemes in combination with high order finite element method.The numerical results show that for polynomials of degree 2 semi-Lagrangian schemes are faster than Lagrange-Galerkin schemes for the same number of degrees of freedom,however,for the same level of accuracy both methods are about the same in terms of CPU time.For polynomials of degree larger than 2,Lagrange-Galerkin schemes behave better than semi-Lagrangian schemes in terms of both accuracy and CPU time;specially,for polynomials of degree 8 or larger.Also,we have performed tests on the parallelization of these schemes and the speedup obtained is quasi-optimal even with more than 100 processors.
文摘In this article,a Crank-Nicolson/Explicit scheme is designed and analyzed for the time-dependent natural convection problem with nonsmooth initial data.The Galerkin finite element method(FEM)with stable MINI element is used for the velocity and pressure and linear polynomial for the temperature.The time discretization is based on the Crank-Nicolson scheme.In order to simplify the computations,the nonlinear terms are treated by the explicit scheme.The advantages of our numerical scheme can be list as follows:(1)The original problem is split into two linear subproblems,these subproblems can be solved in each time level in parallel and the computational sizes are smaller than the origin one.(2)A constant coefficient linear discrete algebraic system is obtained in each subproblem and the computation becomes easy.The main contributions of this work are the stability and convergence results of numerical solutions with nonsmooth initial data.Finally,some numerical results are presented to verify the established theoretical results and show the performances of the developed numerical scheme.
基金the NSF of China(No.10971166)the National High Technology Research and Development Program of China(863 Program,No.2009AA01A135).
文摘This paper is concerned with a stabilized finite element method based on two local Gauss integrations for the two-dimensional non-stationary conductionconvection equations by using the lowest equal-order pairs of finite elements.This method only offsets the discrete pressure space by the residual of the simple and symmetry term at element level in order to circumvent the inf-sup condition.The stability of the discrete scheme is derived under some regularity assumptions.Optimal error estimates are obtained by applying the standard Galerkin techniques.Finally,the numerical illustrations agree completely with the theoretical expectations.
文摘We develop a new sixth-order accurate numerical scheme for the solution of two point boundary value problems.The scheme uses nonpolynomial spline basis and high order finite difference approximations.With the help of spline functions,we derive consistency conditions and it is used to derive high order discretizations of the first derivative.The resulting difference schemes are solved by the standard Newton’s method and have very small computing time.The new method is analyzed for its convergence and the efficiency of the proposed scheme is illustrated by convection-diffusion problem and nonlinear Lotka–Volterra equation.The order of convergence and maximum absolute errors are computed to present the utility of the new scheme.
基金Supported by the National Natural Science Foundation of China(21206009)Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality(PHR201107123)Program for Doctoral Fund in Beijing University of Civil Engineering and Architecture(101102307)
文摘This study is focused on a steady dissipative layer, which is generated by Marangoni convection flow over the surface resulted from an imposed temperature gradient, coupled with buoyancy effects due to gravity and external pressure. A model is proposed with Marangoni condition in the boundary conditions at the interface. The similarity equations are determined and approximate analytical solutions are obtained by an efficient transformation, asymptotic expansion and Pade approximant technique. For the cases that buoyancy force is favorable or unfavor-able to Marangoni flow, the features of flow and temperature fields are investigated in terms of Marangoni mixed convection parameter and Prantl number.
文摘Hot air producing is one of the most important engineering applications in recent years.It is a technique used in various thermodynamic systems,such as home heating systems,food dryers.One of the main problems impeding the spread of hot air producing technology is the lack of homogeneity of the heat flow coming from hot air generators as well as an inadequate flow rate.The most of the existing hot air generators require to be supported by systems that can increase the low volumetric flow and the air temperature of these generators,through increasing the speed of the flow of air emitted or lifting the drawer Heat,which contributes to raising the overall cost.However,to improve the thermal and dynamic quality of the hot air flow produced by the generator,a numerical investigation of the free convection flow inside two different configurations is presented in this thesis.The primary objective of this work is to predict the behavior of the flow inside tow configurations,the first one consists of a vertical cylinder with heated walls,and the second configuration is an open-ended vertical cylinder with a hot disc placed at the entrance(configuration A,configuration B).This work characterizes through the examination of this flow,the variables that control an air emission with high flow rate and a high and homogeneous temperature to represent the appropriate criteria that should be respected to obtain a hot air generator overcoming the previously mentioned constraints.Furthermore;the results of this work show the influence the boundary conditions and Rayleigh number on the resulting flow.
基金supported by the National Science Foundation (No.DMS0606671)a 111 project from the Chinese MOE
文摘It is well-known that physical laws for large chaotic dynamical systems are revealed statistically.Many times these statistical properties of the system must be approximated numerically.The main contribution of this manuscript is to provide simple and natural criterions on numerical methods (temporal and spatial discretization) that are able to capture the stationary statistical properties of the underlying dissipative chaotic dynamical systems asymptotically.The result on temporal approximation is a recent finding of the author,and the result on spatial approximation is a new one.Applications to the infinite Prandtl number model for convection and the barotropic quasi-geostrophic model are also discussed.
基金supported by the National Natural Science Foundation of China(Nos.11701253,11971259,11801216)Natural Science Foundation of Shandong Province(No.ZR2017BA010)。
文摘In this paper,we investigate a stochastic meshfree finite volume element method for an optimal control problem governed by the convection diffusion equations with random coefficients.There are two contributions of this paper.Firstly,we establish a scheme to approximate the optimality system by using the finite volume element method in the physical space and the meshfree method in the probability space,which is competitive for high-dimensional random inputs.Secondly,the a priori error estimates are derived for the state,the co-state and the control variables.Some numerical tests are carried out to confirm the theoretical results and demonstrate the efficiency of the proposed method.
