定常不可压Navier-Stokes型方程的非线性Galerkin有限元算法的收敛性

给出数值求解二维定常不可压Navier-Stokes型方程的非线性Galerkin有限元算法,并分析了数值解的正则性和收敛性,当粗网格参数H和细网格参数h满足关系式H=O(h^1/2)时,该算法具有和Galerkin有限元算法同阶的收敛精度,然而在计算上比Galerkin有限元算法更为简单,可以节省可观的计算量.最后给出了数值试验,验证了上述结果。     

Mixed Initial Boundary-value Problem for Some Multidimensional Nonlinear Schrodinger Equations Including Damping

The motivation of this paper is the study of the unique existence of weak and smooth solutions for the mixed initial boundary-value problem of some multidimensional nonlinear Schrödinger equations induding damping.     

哑铃式聚合物分子模型流变学数值研究

本文介绍了求解哑铃式分子模型位形空间分布函数扩散方程的数值方法,以及用这种方法计算的若干分子模型的流变性质。在通常情况下,将这一方法与求解流动守恒方程的边界元法相结合,便有可能用一个得不到本构方程的分子模型去代替连续介质力学本构方程,来模拟聚合物流体的复杂流动。本文还讨论了这一方法某些令人感兴趣的特点。      

One-dimensional nonuniform temperature flow with heat transfer by convection

In ref. [1], V. E. Najenov studied the conditions that when the viscosity of the liquid is an exponential function of temperature, the pipe flow, having steady heat transfer, is one dimensional and with nonuniform temperature. For plane canal and circular pipe he still studied the velocity and the temperature fields.In this paper, the author presents two new methods for solving the same problem. The method as in ref. [1] may be regarded as the natural branch of the methods of this paper. One of our new methods only can solve the same problem as in ref. [1] and the complex degree of its computing process is nearly the same as that in ref. [1]. But the other can go beyond the studying scope of ref. [1], namely, for the case that the curvatures of circumference of the cross section of the pipe are not equivalent everywhere, the problem may also be solved.     

NEW THEORY FOR EQUATIONS OF NON-FUGHSIAN TYPE REPRESENTATION THEOREM OF TREE SERIES SOLUTION (Ⅰ)

In the analytic theory of differential equations the exact explicit analytic solution has not been obtained for equations of the non-Fuchsian type (Poincare's problem). The new theory proposed in this paper for the first time affords a general method of finding exact analytic expres-sion for irregular integrals.By discarding the assumption of formal solution of classical theory,our method consists in deriving a cor-respondence relation from the equation itself and providing the analytic structure of irregular integrals naturally by the residue theorem. Irregular integrals are made up of three parts: noncontracted part,represented by ordinary recursion series,all-and semi-contracted part by the so-called tree series. Tree series solutions belong to analytic function of the new kind with recursion series as the special case only.     

THE FINITE ELEMENT METHOD FOR SEMILINEAR PARABOLIC EQUATIONS WITH DISCONTINUOUS COEFFICIENTS

1.IntroductionLetxbepointsonplaneR',andfibeapolygonaldomain,wedenotetheboundaryoffibyOff.Thereinfiarefinitemanybrokelineswhichdivideitilltofinitepolygonalsubdomainsall,I=1,''jL.Thefunctionp(x)EL'(fl)isassumedtohaveboundedfirstderivativesinallsubdomainsall,whilepisallowedtobediscontinuousontheinterfacesoflinOflj.AndthereexistsapositiveconstantTsuchthatp(x)2T)Vxefi.WeadopttheusualnotationsoftheSobolevspacesinthispaper,thatis,denotebyH'(fl)andHI(fl)thespacesand11'11.thenorms,l'1.theseminor…     

A mixed galerkin method for computing the flow between eccentric rotating cylinders

A mixed Galerkin technique with B-spline basis functions is presented to compute two-dimensional incompressible flow in terms of the primitive variable formulation. To circumvent the Babuska–Brezzi stability criterion, the artificial compressibility formulation of the equation of mass conservation is employed. As a result, the diagonal components of the matrix form in the governing equations are not singular. The B-spline basis is used because it is superior to other splines in providing computer solutions to fluid flow problems. One of the advantages of the B-spline basis is that it has excellent approximation properties. Numerical examples of applications of the mixed formulation are presented to demonstrate the convergence characteristics and accuracy of the present formulation. © 1998 John Wiley & Sons, Ltd.     

A numerical study on flow through the spiral casing of a hydraulic turbine

Flow through the spiral casing of a hydraulic turbine was analyzed. Reynolds averaged Navier–Stokes equations were solved using a finite element method. The physical domain was divided into a number of hexahedral elements which are isoparametrically mapped onto standard cubic elements. Numerical integration for the unsteady momentum equation is performed over such hexahedral elements to obtain a provisional velocity field. Compliance with the mass conservation equation and determination of the pressure correction are accomplished through an iterative procedure. The velocity distribution inside the spiral casing corroborates the results available in literature. The static pressure at the midplane generally decreases from the outside wall towards the exit of the spiral casing. © 1998 John Wiley & Sons, Ltd.     

Finite volumes and mixed Petrov‐Galerkin finite elements: The unidimensional problem

For Laplace operator in one space dimension, we propose to formulate the heuristic finite volume method with the help of mixed Petrov‐Galerkin finite elements. Weighting functions for gradient discretization are parameterized by some function ψ : [0, 1] → ℝ. We propose for this function ψ a compatibility interpolation condition, and we prove that such a condition is equivalent to the inf‐sup property when studying stability of the numerical scheme. In the case of stable scheme and under two distinct hypotheses concerning the regularity of the solution, we demonstrate convergence of the finite volume method in appropriate Hilbert spaces and with optimal order of accuracy. © 2000 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 16: 335–360, 2000     

轴向变速运动粘弹性弦线横向振动的复模态Galerkin方法

在考虑初始张力和轴向速度简谐涨落的情况下,利用含预应力三维变形体的运动方程,建立了轴向变速运动弦线横向振动的非线性控制方程,材料的粘弹性行为由Kelvin模型描述．利用匀速运动线性弦线的模态函数构造了变速运动非线性弦线复模态Galerkin方法的基底函数,并借助构造出来的基底函数研究了复模态Galerkin方法在轴向变速运动粘弹性弦线非线性振动分析中的应用．数值结果表明,复模态Galerkin方法相比实模态Galerkin方法对变系数陀螺系统有较高的收敛速度．