A WAVE EQUATION MODEL TO SOLVE THE MULTIDIMENSIONAL TRANSPORT EQUATION

The wave equation model, originally developed to solve the advection–diffusion equation, is extended to the multidimensional transport equation in which the advection velocities vary in space and time. The size of the advection term with respect to the diffusion term is arbitrary. An operator-splitting method is adopted to solve the transport equation. The advection and diffusion equations are solved separate ly at each time step. During the advection phase the advection equation is solved using the wave equation model. Consistency of the first-order advection equation and the second-order wave equation is established. A finite element method with mass lumping is employed to calculate the three-dimensional advection of both a Gaussian cylinder and sphere in both translational and rotational flow fields. The numerical solutions are accurate in comparison with the exact solutions. The numerical results indicate that (i) the wave equation model introduces minimal numerical oscillation, (ii) mass lumping reduces the computational costs and does not significantly degrade the numerical solutions and (iii) the solution accuracy is relatively independent of the Courant number provided that a stability constraint is satisfied. © 1997 by John Wiley & Sons, Ltd.     

EXISTENCE OF POSITIVE RADIAL SOLUTIONS FOR SOME SEMILINEAR ELLIPTIC EQUATIONS IN ANNULUS

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｓｔｕｄｉｅｓｏｆｐｏｓｉｔｉｖｅｒａｄｉａｌｓｏｌｕｔｉｏｎｓｆｏｒｆｏｌｌｏｗｉｎｇｓｅｍｉｌｉｎｅａｒｅｌｌｉｐｔｉｃｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍ(Ｐ)　Δｕ(Ｘ) +ｇ( ｜Ｘ｜)ｆ(ｕ(Ｘ) ) =0 ,　　Ｒ1<｜Ｘ｜<Ｒ2 ,ｕ(Ｘ) ｜｜Ｘ｜ =Ｒ1 =ｕ(Ｘ) ｜｜Ｘ｜ =Ｒ2 =0(ｗｈｅｒｅＲ1>0 ,Ｘ ∈Ｒｎ,ｎ ≥ 2 )ａｒｅｂｅｉｎｇｃｏｎｔｉｎｕｅｄｆｏｒｒｅｃｅｎｔ 2 0ｙｅａｒｓｗｉｔｈｏｕｔｉｎｔｅｒｒｕｐｔｉｏｎ[1- 11],ｂｅｃａｕｓｅｔｈｅｐｒｏｂｌｅｍ (Ｐ)ｈａｓｗｉ…     

Spectral method for semilinear parabolic integrodifferential equations

ＳＰＥＣＴＲＡＬＭＥＴＨＯＤＦＯＲＳＥＭＩＬＩＮＥＡＲＰＡＲＡＢＯＬＩＣＩＮＴＥＧＲＯＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＬｉｕＸｉａｏ－ｑｉｎｇ（刘小清）ＷｕＳｈｅｎｇ－ｃｈａｎｇ（吴声昌）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａ...     

On diffusion velocity and the mass conservation equation for components

The mass migration velocity(absolute velocity)of component i in a multicomponent flow is equal to the convection velocity(frame velocity)plus the diffusion velocity(relativevelocity).The diffusion velocity as well as the corresponding diffusion coefficient depends on how the convection velocity is adopted.In turbulent flow,the mass migration velocity of component i is(?)(mass-weighted time average velocity).The diffusion velocity(-a)consists of turbulent diffusionvelocity(?)and molecular diffusion velocity(?)(?is the simple time average velocity of component i and a is a certain convection velocity).So,the part of turbulent diffusion velocity is independent of what convection velocity is taken.In the mass conservation equation for component i,the expression for the diffusion term on its right-hand side will change when the convection velocity on its left-hand side changes.In turbulent flow,there could be no diffusion terms,or a turbulent diffusion term only,or both the turbulent and molecular diffusion     

JB-9014炸药超压爆轰产物的状态方程

根据P.K.Tang等提出的对炸药爆轰产物超压状态方程建模时只对JWL状态方程CJ等熵线中 高压指数项做修正的研究思路,首先给定超压状态下内能等熵线的修正项,再根据热力学定律对内能等熵线 求微分而得到沿压力等熵线的修正项。对JB-9014炸药超压爆轰冲击Hugoniot实验数据和声速实验数据同 时进行拟合,得到了3个JWL状态方程在超压爆轰状态下的修正项,并进行了分析与比较。得到超压修正项 的方法简单,3组超压修正项与P.K.Tang的修正项一样,都能很好地拟合超压Hugoniot数据。在实验数据 范围外,对超压状态下的声速-压力实验数据的拟合精度有所差别。     

Constitutive equation for dilute polymer solutions in strong elongational flow

A constitutive equation is proposed, which is constructed using both phenomenological and structural ideas. In this formulation, the kinematics of the fluid is characterized by the deformation rate and a structural vector. The vector follows an evolutionary law which is inspired by known molecular models. The expression for the stress is given by introducing a dissipative term related to the strong hydrodynamic interaction of the distorted molecules and a deformation term for the molecules, as well as by using the second law of thermodynamics.A study of the general properties of the evolutionary equation and its response in a homogeneous two-dimensional flow provides evidence of the performance of the proposed model.     

Blow-up rate estimate for degenerate parabolic equation with nonlinear gradient term

Abstract In this paper, the blow-up rate is obtained for a porous medium equation with a nonlinear gradient term and a nonlinear boundary flux. By using a scaling method and regularity estimates of parabolic equations, the blow-up rate determined by the interaction between the diffusion and the boundary flux is obtained. Compared with previous results, the gradient term, whose exponent does not exceed two, does not affect the blow-up rate of the solutions.     

Nonconforming local projection stabilization for generalized Oseen equations

A new method of nonconforming local projection stabilization for the gen- eralized Oseen equations is proposed by a nonconforming inf-sup stable element pair for approximating the velocity and the pressure. The method has several attractive features. It adds a local projection term only on the sub-scale （H ≥ h）. The stabilized term is simple compared with the residual-free bubble element method. The method can handle the influence of strong convection. The numerical results agree with the theoretical expectations very well.     

Boussinesq方程的发展形式与Airy波理论差异性研究

应用势流理论，采用递推函数方法推导出一个新形式的Ｂｏｕｓｉｎｅｓｑ方程。通过对新方程的参数设置，可以讨论出Ｂｏｕｓｓｉｎｅｓｑ方程发展趋势和不同的发展形式。对浅水波动的描述方程，Ｂｏｕｓｓｉｎｅｓｑ方程的发展趋势为适用水深范围的拓展。拓展应用范围的大小则由其方程频散特征向Ａｉｒｙ波频散解逼近程度来决定。而Ｂｏｕｓｉｎｅｑ方程又不同于Ａｉｒｙ波，主要原因是Ｂｏｕｓｓｉｎｅｓｑ方程中含有线性频散项，Ａｉｒｙ波则只是长波首项近似，无线性频散项。其频散特征为精确的线性频散解。对实际水波传播而言，Ａｉｒｙ波理论的局限性是不言而喻的。     

The parameter perturbation method on elastic wave equation in inhomogeneous medium

I.IntroductionTheelasticwaveininhomogeneousmediumiscomplicatedbecauseofthediffracting,scattering,andtransmutingofthewavetapes.Exceptforsomesimpleandregularmediummode1s,thesolutionofelasticwavehasnotbeengotyet.Nowadays,theresearchoftheelasticwavescattering…     

用材料力学公式计算任意截面短梁正应力时的修正项研究

对材料力学中梁的弯曲应力公式增加一修正项,以反映短梁弯剪翘曲变形对应力分布的影响。提出一种根据短梁横截面边界形状及艾瑞应力函数求解应力修正项的方法,应用弹性力学空间问题的一般理论,通过应力平衡方程、应变相容方程及应力边界条件,建立了关于任意截面短梁的应力修正项及剪应力的基本方程。在所建立的基本方程基础上,导出了矩形截面和圆形截面短梁修正应力的具体计算公式,该修正应力与均布荷载大小及弹性模量与剪切模量之比均成正比,但与截面惯性矩成反比。数值算例表明,本文方法计算的应力与通用有限元软件ANSYS计算的结果吻合良好,从而验证了本文方法及其基本公式的正确性。     

流动稳定性理论中空间模式不稳定波能量方程中的一个问题

文中指出在有关流动稳定性的文献中,对空间模式问题所用的能量方程有一个小的,但却是很重要的错误。     

Uniform blow-up rate for compressible reactive gas model

The Dirichlet initial-boundary value problem of a compressible reactive gas model equation with a nonlocal nonlinear source term is investigated. Under certain conditions, it can be proven that the blow-up rate is uniform in all compact subsets of the domain, and the blow-up rate is irrelative to the exponent of the diffusion term, however, relative to the exponent of the nonlocal nonlinear source.     

NUMERICAL SIMULATION OF WING-BODY JUNCTION TURBULENCE FLOW

Wing-body junction turbulence flow is simulated by using RANS equation and boundary fitted coordinate technique.Three order differential scheme is used in the computation of convection term and two layers turbulence model are employed in the calculation.     

伯努利方程教学设计中的若干问题1)

针对流体力学课程中伯努利方程内容的教学设计,分析了伯努利方程演示实验中的常见误解,提供了伯努利方程的不同推导方法,讨论了方程中压强项的物理意义,并将伯努利方程进一步联系拓展,以加深学生的理解认识,建立科学严谨的分析方法。伯努利方程的推导是我们认识该方程最基本的出发点,在运用伯努利方程对演示实验解释时一定要注意伯努利方程的适用条件,且综合考虑流体黏性、卷吸等因素的影响。大多数中文教材和英文教材关于伯努利方程中压强项的物理意义解读不同,由伯努利方程推导过程可知,方程中的压强项具有势能的特性,这一特性仅对流体成立。通过建立伯努利方程与其他知识点的联系,对比了可压缩和不可压缩伯努利方程的形式,加深了学生对伯努利方程的理解认识。     

非惯性坐标系中的边界层方程

本文用匹配渐近展开法导出二维翼型在非惯性坐标系中的一阶和二阶边界层方程,消去压强项后,一阶边界层方程与经典边界层方稃相同;惯性力的作用在二阶边界层中才出现。     

Studies of nonlinear theories for thin shells

In order to formulate the equations for the study here, the Fourier expansions upon the system of orthonormal polynomials areused.It may be considerably convenient to obtain the expressions of displacements as well as stresses directly from the solutions.Based on the principle of virtual work the equilibrium equations of various orders are formulated. In particular, the system of third-order is given in detail, thus providing the reference for accuracy analysis of lower-order equations. A theorem about the differentiation of Legendre series term by term is proved as the basis of mathematical analysis. Therefore the functions used are specified and the analysis rendered is no longer a formal one.The analysis will show that the Kirchhoff-Love’s theory is merely of the first-order and the theory which includes the transverse deformation but keeps the normal straight is essentially of the first order, too.     

Derivation of a second-order model for Reynolds stress using renormalization group analysis and the two-scale expansion technique

With the two-scale expansion technique proposed by Yoshizawa,the turbulent fluctuating field is expanded around the isotropic field.At a low-order two-scale expansion,applying the mode coupling approximation in the Yakhot-Orszag renormalization group method to analyze the fluctuating field,the Reynolds-average terms in the Reynolds stress transport equation,such as the convective term,the pressure-gradient-velocity correlation term and the dissipation term,are modeled.Two numerical examples:turbulent flow past a backward-facing step and the fully developed flow in a rotating channel,are presented for testing the efficiency of the proposed second-order model.For these two numerical examples,the proposed model performs as well as the Gibson-Launder (GL) model,giving better prediction than the standard k-ε model,especially in the abilities to calculate the secondary flow in the backward-facing step flow and to capture the asymmetric turbulent structure caused by frame rotation.     

Improved non‐staggered central NT schemes for balance laws with geometrical source terms

In this paper we extend the non‐staggered version of the central NT (Nessyahu–Tadmor) scheme to the balance laws with geometrical source term. This extension is based on the source term evaluation that includes balancing between the flux gradient and the source term with an additional reformulation that depends on the source term discretization. The main property of the scheme obtained by the proposed reformulation is preservation of the particular set of the steady‐state solutions. We verify the improved scheme on two types of balance laws with geometrical source term: the shallow water equations and the non‐homogeneous Burger's equation. The presented results show good behaviour of the considered scheme when compared with the analytical or numerical results obtained by using other numerical schemes. Furthermore, comparison with the numerical results obtained by the classical central NT scheme where the source term is simply pointwise evaluated shows that the proposed reformulations are essential. Copyright © 2004 John Wiley & Sons, Ltd.     

基于雷诺应力模型的平衡大气边界层模拟

基于雷诺应力湍流模型（简称RSM模型）,研究了平衡大气边界层风场数值模拟问题．假设流体不可压,且不计雷诺应力输运方程中的对流项、浮力产生项、系统旋转产生项和扩散项,在准各向同性的条件下,推导出RSM模型湍动能k的表达式是标准k-ε模型k常数表达式的0.893倍．考虑k沿高度变化的修正,根据在标准k-ε模型中满足水平均匀性的湍流来流边界条件,提出在RSM模型中产生平衡大气边界层的湍流来流边界条件．基于空风洞的数值模拟结果表明,与工程上常用的湍流来流边界条件相比,基于本文提出的湍流来流边界条件得到的风场水平均匀性更优,且在整个流域内,得到的雷诺应力剖面更合适．从而验证了该湍流来流边界条件的适用性．