论简化Navier-Stokes方程组(SNSE)

本文论述简化 Navier-Stokes 方程组(SNSE),利用十种 SNSE分析Jeffery-Hamel流动并简要分析已知完全 Navier-Stokes 方程组(CNSE)精确解的八类流动。表明:不同SNSE结果之间的实际差异能够大大超出O(Re~(-1/2))量级的理论误差范围,甚至给出不同的流动图案。因此,SNSE 的粘性项如何取舍值得重视。内外层匹配SNSE和薄层二阶SNSE的解在八类流动情况下均与CNSE的精确解完全一致;而所有其它SNSE 的解则与CNSE的精确解不完全一致,它们的解在不少情况下实际就是经典边界层理论的解。内外层匹配SNSE包含了法向轴相对流向轴剪切的剪应力项和法向轴伸缩的法应力项以及与该法应力项同量级的粘性项,且对惯性项和粘性-惯性项相互关系的处理较合理,故在力学上和数学上都比较可取。

Stokes流的积分方程法

<正> Stokes流,或称零雷诺数流,指的是尺寸微小、速度缓慢的流动。它的理论在化工、生物力学、物理化学、环境保护、选矿、地球物理和气象科学等各个领域都有重要的应用。 零雷诺数流可用Stokes方程来描述:式中μ,V和P分别是流体的粘度、速度向量和压力。直到本世纪60年代,只有数目非常有

简化Navier-Stokes方程组(SNSE)的几个精确解

对不可压二维驻点流、三维驻点流和旋转圆盘附近的流动等三种流动情况,本文给出简化Navier-Stokes方程组(SNSE)及其精确解。表明:文献[1]理论的SNSE的精确解,在三种流动情况下均与完全Navier-Stokes方程组(NSE)的精确解完全一致;文献[3]SNSE的精确解的速度解与完全NSE精确解的速度解一致,但压力解在三种流动情况下均与完全NSE精确解的压力解不同。文献[3]SNSE精确解给出的压力分布相对与完全NSE精确解给出的压力分布的最大相对误差为100％。

三维简化Navier-Stokes方程的最优形式

<正> 引言 最近十多年,简化NS方程(以下记为SNS)的研究和计算有长足进展。由于在NS方程组中对粘性项的取舍不同,因而有几种不同的简化NS方程组,究竟哪种形式更合理,是需进一步探讨的一个问题。文献[1]利用原始NS方程及三种不同的简化NS方程组,对球的超音速绕流数值试验表明,其效果是不一样的。文献[3]也指出,如果SNS方程组的形式选择不当,会带来不可忽略的误差。从二维研究不难看出,目前广泛采用的三维SNS方程即粘性激波层方程组(VSL)及抛物化NS方程组(PNS),都不是最合理的简化形式。本文提出三维NS方程组的一种最好形式,称为修正的PNS方程组(记为MPNS),并论证它的合理性及精确度。

ADI方法求解Navier-Stokes方程的一个改进格式

ADI方法常被用来计算不可压缩Navier-Stokes方程。在处理涡度方程的非线性项和涡度在壁面上的条件时,通常采用滞后的方法对涡度方程和流函数方程分别求解。然而,非线性项的滞后破坏了ADI方法的完全二阶精度;涡度方程和流函数方程分别求解减弱了两个方程的耦合性;涡度壁面条件的滞后则破坏了方法的完全隐式。本文在应用ADI方法求解涡度方程和流函数方程时应用了一种交替线性化的技术,对涡度方程和流函数方程耦合求解,内点和边界点上的涡度和流函数值同时求出。因此,ADI方法保持了完全的二阶精度,避免了上面所提到的问题。作者应用这一方法计算了雷诺数R_θ等于1,10,100,500,1000时的二维方腔流动(空间步长h=1/20)。计算结果表明:这一方法保持了通常ADI方法的优点,可以应用大的时间步长。最后补充计算了雷诺数R_θ=2000的二维方腔流动。

简化Navier-Stokes方程组及无粘和粘性边界层联合求解

<正> 简化N-S方程组具有抛物-双曲方程组的特性,对定常情况可用向前推进的计算方法,要比数值求解椭圆型完全N-S方程组简单得多;求解简化N-S方程组能够同时算出无粘外部流和粘性边界层流,理论上要比先算无粘流、然后再算粘性边界层流的常规方法

简化Navier-Stokes方程组及其数学性质

本文对二绝简化Navier-stokes方程组作了定性分忻,作者认为当流动的切向速度分量u

Thermal stress wave and spallation induced by an electron beam

Thermal stress wave and spallation in aluminium alloy exposed to a high fluency and low energy electron beams are studied theoretically. A simple model for the study of energy deposition of electrons in materials is presented on the basis of some empirical formulae. Under the stress wave induced by energy deposition, microcracks and/or microvoids may appear in target materials, and in this case, the inelastic volume deformation should not vanish. The viscoplastic model proposed by Bodner and Partom with corresponding Gurson's yield function requires modification for this situation. The new constitutive model contains a scalar field variable description of the material damage which is taken as the void volume fraction of the polycrystalline material. Incorporation of the damage parameter permits description of rate-dependent, compressible, inelastic deformation and ductile fracture. The melting phenomenon has been observed in the experiment, therefore one needs to take into account the melting process in the intermediate energy deposition range. A three-phase equation of state used in the paper provides a more detailed and thermodynamical description of metals, particularly, in the melting region. The computational results based on the suggested model are compared with the experimental test for aluminium alloy, which is subjected to a pulsed electron beam with high fluency and low energy. (C) 1997 Elsevier Science Ltd.

Wave pattern characteristics of a two-phase nozzle flow by shock propagation

In this paper, the wave pattern characteristics of shock-induced two-phase nozzle Hows with the quiescent or moving dusty gas ahead of the incident-shock front has been investigated by using high-resolution numerical method. As compared with the corresponding results in single-phase nozzle flows of the pure gas, obvious differences between these two kinds of flows can be obtained.

Compact finite difference - Fourier spectral method for three-dimensional incompressible Navier-Stokes equations

A new compact finite difference-Fourier spectral hybrid method for solving the three dimensional incompressible Navier-Stokes equations is developed in the present paper. The fifth-order upwind compact finite difference schemes for the nonlinear convection terms in the physical space, and the sixth-order center compact schemes for the derivatives in spectral space are described, respectively. The fourth-order compact schemes in a single nine-point cell for solving the Helmholtz equations satisfied by the velocities and pressure in spectral space is derived and its preconditioned conjugate gradient iteration method is studied. The treatment of pressure boundary conditions and the three dimensional non-reflecting outflow boundary conditions are presented. Application to the vortex dislocation evolution in a three dimensional wake is also reported.

Parameter-transformation relations for traveling-wave solutions of kdv-burgers equation

 Burgers suggested that the main properties of free-turbulence in the boundless area without basic flow might be understood with the aid of the following equation, which was much simpler than those of fluid dynamics, 更多还原

Reflection of shock-wave in pur foam from rigid wall

Keller proposed that a building, a mechanical installation or a body wrapped bya layer of foam plastics may be an efficient means for protection from damage ofblast wave. However, the practical effect was beyond expectation. For example, agunner wearing the foam plastics-padded waistcoat was injured more seriously by theblast wave from a muzzle. Monti took the foam plastics as homogeneous two-phasemedium and analyzed it with the theory of dusty flow. The obtained results showthat the peak pressure behind the reflected shock wave from rigid wall with foamcoat exceeds obviously that without foam coat under the same condition. Gel'fand,Patz and Weaver made experimental observations by means of shock tubes and veri-

3-dimensional transient wave response in a cracked elastic solid

The three-dimensional transient wave response problem is presented for an infinite elastic medium weakened by a plane crack of infinite length and finite width. Tractions are applied suddenly to the crack, which simulates the case of impact loading. The integral transforms are utilized to reduce the problem to a standard Fredholm integral equation in the Laplace transform variable and sequentially invert the Laplace transforms of the stress components by numerical inversion method. The dynamic mode I stress intensity factors at the crack tip are obtained and some numerical results are presented in graphical form.