The penalty and hybrid methods are being much used in dealing with the general incompatible element, With the penalty method convergence can always be assured, but comparatively speaking its accuracy is lower, and the...The penalty and hybrid methods are being much used in dealing with the general incompatible element, With the penalty method convergence can always be assured, but comparatively speaking its accuracy is lower, and the condition number and sparsity are not so good. With the hybrid method, convergence can be assured only when the rank condition is satisfied. So the construction of the element is extremely limited. This paper presents the mixed hybrid penalty element method, which combines the two methods together. And it is proved theoretically that this new method is convergent, and it has the same accuracy, condition number and sparsity as the compatible element. That is to say, they are optimal to each other.Finally, a new triangle element for plate bending with nine freedom degrees is constructed with this method (three degreesof freedom are given on each corner -- one displacement and tworotations), the calculating formula of the element stiffness matrix is almost the same as that of the old triangle element for plate bending with nine degrees of freedom But it is converged to true solution with arbitrary irregrlar triangle subdivision. If the true solution u?H3 with this method the linear and quadratic rates of convergence are obtianed for three bending moments and for the displacement and two rotations respectively.展开更多
In this paper, a new finite element method for the flow analysis of the viscous incompressible power-law fluid is proposed by the use of penalty-hybrid/mixed finite element formulation and by the introduction of an al...In this paper, a new finite element method for the flow analysis of the viscous incompressible power-law fluid is proposed by the use of penalty-hybrid/mixed finite element formulation and by the introduction of an alternative perturbation, which is weighted by viscosity, of the continuity equation. A numerical example is presented to exhibit the efficiency of the method.展开更多
The two-level penalty mixed finite element method for the stationary Navier-Stokes equations based on Taylor-Hood element is considered in this paper. Two algorithms are proposed and analyzed. Moreover, the optimal st...The two-level penalty mixed finite element method for the stationary Navier-Stokes equations based on Taylor-Hood element is considered in this paper. Two algorithms are proposed and analyzed. Moreover, the optimal stability analysis and error estimate for these two algorithms are provided. Finally, the numerical tests confirm the theoretical results of the presented algorithms.展开更多
In this paper, the internal fluid motion of a jet system is described by the Navier Stokes mechanics equations. For the simulation of the motion, the penalty function finite element method is used, and the velocity ve...In this paper, the internal fluid motion of a jet system is described by the Navier Stokes mechanics equations. For the simulation of the motion, the penalty function finite element method is used, and the velocity vectors and stream function curves are obtained. Using the Prandtl theory, this paper derives the free jet velocity and the jet bunch width in a half-space, the latter of which is amended by experiment. The results obtained in this paper are applied to micro-type high pressure water jet cleaner and the ejector of rocket engine.展开更多
A penalty function upwind finite element method is describe in this paper for diffusive convection problem in temperature and salinity double-diffusive system. With good stability and two-order accuracy, the method wa...A penalty function upwind finite element method is describe in this paper for diffusive convection problem in temperature and salinity double-diffusive system. With good stability and two-order accuracy, the method was directly employed to the original equations,and tested in a square cavity with constant lateral heating. The steady-state results are approximate to the tendency of the time-dependent results by pressure-velocity (PV) coupling method. Nunerical simulation in a square cavity with adiabatic baffle and constant lateral heating was achieved with distribution of stream function, temperature and concentration isocontours under Thermal Raleigh Number Re= 106 and the thermal buoyancy ratio covering the ramp of N = 1, 3, 5, 7. Meanwhile, the effects of N and the adiabatic baffle to the fluid field were ho discussed.展开更多
文摘The penalty and hybrid methods are being much used in dealing with the general incompatible element, With the penalty method convergence can always be assured, but comparatively speaking its accuracy is lower, and the condition number and sparsity are not so good. With the hybrid method, convergence can be assured only when the rank condition is satisfied. So the construction of the element is extremely limited. This paper presents the mixed hybrid penalty element method, which combines the two methods together. And it is proved theoretically that this new method is convergent, and it has the same accuracy, condition number and sparsity as the compatible element. That is to say, they are optimal to each other.Finally, a new triangle element for plate bending with nine freedom degrees is constructed with this method (three degreesof freedom are given on each corner -- one displacement and tworotations), the calculating formula of the element stiffness matrix is almost the same as that of the old triangle element for plate bending with nine degrees of freedom But it is converged to true solution with arbitrary irregrlar triangle subdivision. If the true solution u?H3 with this method the linear and quadratic rates of convergence are obtianed for three bending moments and for the displacement and two rotations respectively.
文摘In this paper, a new finite element method for the flow analysis of the viscous incompressible power-law fluid is proposed by the use of penalty-hybrid/mixed finite element formulation and by the introduction of an alternative perturbation, which is weighted by viscosity, of the continuity equation. A numerical example is presented to exhibit the efficiency of the method.
基金This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11271298, 11271313, 61163027）, the Key Project of Chinese Ministry of Education （Grant No. 212197）, the Natural Science Foundation of Xinjiang Province （Grant No. 2013211B01）, and the Doctoral Foundation of Xinjiang University （Grant No. BS120102）.
文摘The two-level penalty mixed finite element method for the stationary Navier-Stokes equations based on Taylor-Hood element is considered in this paper. Two algorithms are proposed and analyzed. Moreover, the optimal stability analysis and error estimate for these two algorithms are provided. Finally, the numerical tests confirm the theoretical results of the presented algorithms.
文摘In this paper, the internal fluid motion of a jet system is described by the Navier Stokes mechanics equations. For the simulation of the motion, the penalty function finite element method is used, and the velocity vectors and stream function curves are obtained. Using the Prandtl theory, this paper derives the free jet velocity and the jet bunch width in a half-space, the latter of which is amended by experiment. The results obtained in this paper are applied to micro-type high pressure water jet cleaner and the ejector of rocket engine.
文摘A penalty function upwind finite element method is describe in this paper for diffusive convection problem in temperature and salinity double-diffusive system. With good stability and two-order accuracy, the method was directly employed to the original equations,and tested in a square cavity with constant lateral heating. The steady-state results are approximate to the tendency of the time-dependent results by pressure-velocity (PV) coupling method. Nunerical simulation in a square cavity with adiabatic baffle and constant lateral heating was achieved with distribution of stream function, temperature and concentration isocontours under Thermal Raleigh Number Re= 106 and the thermal buoyancy ratio covering the ramp of N = 1, 3, 5, 7. Meanwhile, the effects of N and the adiabatic baffle to the fluid field were ho discussed.
