拟流函数法——叶轮机械内三维流动分析问题和设计问题的一种求解方法

本文从动量方程的特点出发并满足连续方程,引入了两个拟流函数.每个拟流函数的主方程均只包含其自身的二阶偏导数,而不包含另一个拟流函数的二阶偏导数.这样,完全的三维解便可通过两个拟流函数主方程的分别单独求解和它们之间的相互迭代来获得.文中给出了在任意非正交坐标系中拟流函数的主方程和相应的边界条件.对叶轮机械内部三维气动分析问题和设计问题的求解进行了讨论和计算,并与解析解、其他数值解法做了比较.结果表明:这种拟流函数方法计算准确而简便,易于得到收敛结果,是求解三维无粘流动的好方法.     

关于一类新型的具边值条件的曲率流问题

本文提出了一类带有边界条件的新的曲率流问题,说明了它们的理论来源和实际背景.对Gauss曲率情形,建立了这种曲率流古典解的存在唯一性,并用一种适用于更一般曲率情形的方法,研究了这种曲率流的渐近性。     

含正三角形孔口热电材料的断裂力学分析

采用复变函数方法研究了含正三角形孔口热电材料中受到无穷远处均匀电流密度和能量流作用下的断裂问题.在电绝缘和热绝缘边界条件下,获得了温度场和应力场的解析表达式,分析了三角形尺寸、能量流载荷对热电材料性能的影响.结果表明,能量流载荷和三角形尺寸的变化对环向能量流、环向应力、环向热流有较明显的影响.     

用区域分解法求不可压N-S方程的差分解

§1.引言 对不可压小粘性流的数值解,[1]和[2]用奇异摄动观点提出了一个区域分解法.从常微分方程(组)的奇异摄动问题出发,解分解为外部解加边界修正解(以下简称为修正解).外部解的边界条件有:给定(原边界条件)、待定(用原边界条件和修正解)和延拓类.修正解的边界条件有:给定(用原边界条件和外部解延拓)渐近(在边界层外缘)和待定     

不可压缩Navier-Stokes方程最优动力系统建模和分析

研究了同时满足任意速度边界条件和速度不可压条件的Navier-Stokes方程最优动力系统的建模方法.通过对方柱绕流问题的最优动力系统的建模与分析,发现该最优动力系统的动力学特性为极限环.同时,该最优动力系统仅使用了三个最优基函数就很好地描述了所有主要的流场特征和该问题的动力学特性,故满足任意速度边界条件和速度不可压条件Navier-Stokes方程最优动力系统的建模方法,能够用最少的基函数最大限度地描述复杂流体问题及其动力学特性.     

一类非线性扩散方程解的blow up速率估计

利用F riedm an-M cleod方法和变动尺度方法研究了一类具有非线性边界条件的非线性扩散方程解的b low up问题,证明了解在有限时间b low up,并且得到了b low up速率估计.     

关于一类新型的具边值条件的曲率流问题

本文提出了一类带有边界条件的新的曲率流问题,说明了它们的理论来源和实际背景对Ｇａｕｓｓ曲 率情形,建立了这种曲率流古典解的存在唯一性,并用一种适用于更一般曲率情形的方法,研究了这 种曲率流的渐近性。     

具有加权非局部边界条件的多孔介质方程组的临界指标问题（英文）

本文研究了具有非局部边界条件和非线性内部源的多孔介质抛物型方程组问题.利用比较原理,获得了权函数和系数对整体解和爆破解的影响,并得到了解的爆破临界指标,推广了先前的研究结果.     

粘滑混合边界条件下平面边界前的Stokes流动

对具有粘滑混合边界条件的平面边界,建立一个Stokes流动的一般性定理,利用双调和函数A与调和函数B,表示了3维Stokes流动的速度场和压力场.关于无滑动平面边界前Stokes流动的早期定理,成为该一般性定理的一个特例.进一步地,从一般性定理导出了一个推论,根据该Stokes流函数,给出了粘滑边界条件时刚性平面轴对称Stokes流动问题的解,得到了流体作用在边界上的牵引力和扭矩公式.给出了一个说明性的例子.     

求解具有混合边界条件的拟线性扩散方程的有限元方法的误差估计问题

在M.F.Wheeler的[5]中,对一类拟线性抛物型方程的F.E.M,进行了颇为深入的理论分析。但是,[5]所考虑的方程,其高阶项的系数,尚有某种局限性,以致不能应用于一般的各向异性问题;对于混合边界的情形,也未加讨论。此外,[5]中所涉及的条件也是较强的,如要求解函数u(x,t)∈c~2(Ω×[0,T])等等。 本文对实践中常常遇到的具有第三混合边界条件的一类拟线性扩散问题的F.E.M,在较[5]为弱的条件下,进行了讨论,把有关拟线性问题的误差估计问题归结为某一线性椭圆边值问题F.E.M的误差估计问题。本文的结果是[1]的推广。     

NUMERICAL SOLUTIONS OF PARABOLIC PROBLEMS ON UNBOUNDED 3-D SPATIAL DOMAIN

In this paper,the numerical solutions of heat equation on 3-D unbounded spatial do-main are considered. n artificial boundary Γ is introduced to finite the computationaldomain.On the artificial boundary Γ,the exact boundary condition and a series of approx-imating boundary conditions are derived,which are called artificial boundary conditions.By the exact or approximating boundary condition on the artificial boundary,the originalproblem is reduced to an initial-boundary value problem on the bounded computationaldomain,which is equivalent or approximating to the original problem.The finite differencemethod and finite element method are used to solve the reduced problems on the finitecomputational domain.The numerical results demonstrate that the method given in thispaper is effective and feasible.     

Clifford分析中多个未知函数向量的非线性边值问题

设fi（x），1≤i≤p为取值在实2n－1维代数An（R）上的函数．我们称F（x）＝（f1，f2，...，fp）为函数向量，而fi，1≤i≤p为向量F的分量，本文借助于向量值分析的思想，利用积分方程方法、Shauder不动点原理和压缩映射原理研究多个未知函数的函数向量F带位移又带共轭值的四元素非线性过值问题解的存在性和相应线性边值问题解的存在唯一性．     

An algebraic foundation for factoring linear boundary problems

Motivated by boundary problems for linear differential equations, we define an abstract boundary problem as a pair consisting of a surjective linear map (“differential operator”) and an orthogonally closed subspace of the dual space (“boundary conditions”). Defining the composition of boundary problems corresponding to their Green’s operators in reverse order, we characterize and construct all factorizations of a boundary problem from a given factorization of the defining operator. For the case of ordinary differential equations, the main results can be made algorithmic. We conclude with a factorization of a boundary problem for the wave equation. This work was supported by the Austrian Science Fund (FWF) under the SFB grant F1322.     

Local boundary dilatation of quasiconformal maps

By studying the existence problem of locally extremal Beltrami differential posed by F. Gardiner and N. Lakic, we introduce a new definition of the local boundary dilatations of points in Teichmuller spaces of simply connected plane domains, which is the same as the usual ones in the case of Jordan domains. Then we show that the answer to the problem of F. Gardiner and N. Lakic is affirmative according to this new definition. Comparing with the usual definitions, the problem of F. Gardiner and N. Lakic is partly answered and the results of G. Cui and Y. Qi is generalized.     

Global regularity of a class of p-fluid flows in cylinders

We consider the motion of an incompressible non-Newtonian fluid with shear dependent viscosity. We extend and improve the results obtained in the recent paper by Crispo [F. Crispo, Shear thinning viscous fluids in cylindrical domains. Regularity up to the boundary, J. Math. Fluid Mech., in press], concerning the case of the motion between two coaxial cylinders, to the case of a full cylinder. Actually we prove boundary regularity for solutions to the stationary Dirichlet problem with zero boundary data.     

奇异两点边值问题正解的存在性

奇异两点边值问题正解的存在性@王俟禹@高文杰...     

双曲型方程具有奇性斜导数的混合问题<英>

本文讨论了2m阶双曲型方程具有奇性斜导数的边值问题。在边界奇点(即不满足Lopatinsky边界条件的点)子流形的一定假设下,证明了所论问题在Sobolev空间H~(s,s)(Q)中解的存在性和唯一性,从而将二阶双曲方程的相应问题的已有的结果(例如[1]、[4—6])推广到了高维的情形。     

Large time behavior of solutions to parabolic equations with Neumann boundary conditions

In this paper we are interested in the large time behavior as t→+∞ of the viscosity solutions of parabolic equations with nonlinear Neumann type boundary conditions in connection with ergodic boundary problems which have been recently studied by Barles and the author in [G. Barles, F. Da Lio, On the boundary ergodic problem for fully nonlinear equations in bounded domains with general nonlinear Neumann boundary conditions, Ann. Inst. H. Poincaré Anal. Non Linèaire 22 (5) (2005) 521-541].     

A robin-neumann problem in bounded domains with splitting boundary

We consider a mixed boundary-value problem for the homogeneous Laplace equation in a bounded domain which boundary splits up into two disjoint smooth components. On the one boundary component we pose a homogeneous Robin condition and an inhomogeneous Neumann condition on the other. We give a weak formulation, interpret this problem as a generalized spectral (eigenvalue) problem in the sense of F.Stummel (cf.[12]) and investigate existence, uniqueness and regularity of weak solutions. This problem is a cut-off version of a basic problem in water-wave theory (cf.Ramm [8], pp.394-395, Simon/Ursell [10] Stoker [11])     

Nonlinear Spatial Evolution of Small Disturbances from Boundary Conditions in Flat Inclined-Channel Flow

The asymptotic behavior of small disturbances as they evolve spatially from boundary conditions in a flat inclined channel is determined. These small disturbances develop into traveling waves called roll waves, first discussed by Dressler in 1949. Roll waves exist if the Froude number F exceeds 2, which consist of a periodic pattern of bores, or discontinuities. After confirming the instability condition for   F > 2  for the linearized equations in the boundary value case, the nonlinear boundary value problem for the weakly unstable region of F slightly larger than 2 is studied. Multiple scales and the Fredholm alternative theorem are applied to determine the evolution of the solution in space. It is found that the solution is dominated by the evolution of the disturbance along one characteristic. The shock conditions governing the asymptotic solution are determined and these conditions are used to determine the approximate shape of the resulting traveling wave from the solution. Both asymptotic and numerical results for periodic disturbances are presented.