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1.
This paper deals with numerical simulation of steady laminar incompressible Newtonian and non-Newtonian fluid flow. The viscosity of non-Newtonian fluid is modelled using the fluid power law. The mathematical model is described by the non-linear conservative system of the incompressible Navier-Stokes equations that is solved using the explicit two-step MacCormack scheme with artificial viscosity together with the pseudo-compressibility method. The spatial discretization is performed by the cell-centred finite volume method on a structured quadrilateral grid. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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This paper deals with the numerical solution of Newtonian and non-Newtonian flows. The flows are supposed to be laminar, viscous, incompressible and steady. The model used for non-Newtonian fluids is some variant of power-law. Governing equations in this model are incompressible Navier-Stokes equations. For numerical solution one could use artificial compressibility method with three stage Runge-Kutta finite volume method in cell centered formulation for discretization of space derivatives. Following cases of flows are solwed: flow through a bypass connected to main channel in 2D and 3D and non-Newtonian flow through branching channels in 2D. These results are presented for 2D and 3D case. This problem could have an application in the area of biomedicine. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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This paper deals with a numerical solution of laminar incompressible steady flows of Newtonian and non–Newtonian fluids through bypass of a restricted vessel. Blood flow is considered to be Newtonian in the case of vessels of large diameters as aorta. On the other hand, with decreasing diameter of a vessel the non–Newtonian behavior of blood can play a significant role. One could describe these problems using Navier–Stokes equations and continuity equation as a model. In the case of Newtonian fluids one considers constant viscosity compared to non–Newtonian fluids where viscosity varies and can depend on the tensor of deformation. In order to find numerical solution, the system of equations is completed using an artificial compressibility method. The space derivatives are discretised using a cell centered finite volume method and arising system of ordinary differential equations is solved using an explicit multistage Runge–Kutta method with given steady boundary conditions. The steady solution is achieved for time t→∞ and steady boundary conditions. The results can be used in the field of cardiovascular research. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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将分形引入渗流力学,建立了分形油藏具有松弛特性的粘弹性液体的不稳定渗流模型;利用双参数( df ,ds) 刻画分形油藏的分形特性,利用四参数(df,ds ,λv ,λp) 描述粘弹性液的广义流动特征;提出了广义的正交变换,并利用Laplace_Weber 变换,拉氏_正交变换给出了无限大地层和有界地层的精确解和渐近解;通过拉氏数值反演和渐近解分析了分形油藏粘弹性液体流动特征· 探讨了改变分形参数时压力变化规律· 相似文献
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非牛顿幂律流体球向不定常渗流 总被引:1,自引:0,他引:1
本文研究了弱压缩非牛顿幂律流体球向不定常渗流,导出了抛物型偏微分非线性方程.球向扩散方程是其特殊情况.用Laplace变换的方法,找到了线性化后方程的解析解和渐近解.用影响半径的概念和平均值方法求得了近似解.渐近解和近似解的结构是相似的,从而丰富了非牛顿流体一维不定常渗流的理论. 相似文献
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This paper is concerned with nonlinear rheological fluids of Oldroyd type. We present a (formal) stability analysis of the corresponding system of equations, showing stability limits on the Weißenberg number in certain cases. Moreover, we introduce a numerical method for solving the full time-dependent Oldroyd system based on the finite element spatial discretization and on the fractional step θ-scheme time approximation. Numerical solutions are presented for two well known benchmark problems: the lid driven cavity and the four-to-one planar contraction. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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聚合物驱油在提高原油采收率方面具有重要作用,水平井在薄层油田的开发过程中占有重要优势.根据聚合物驱油过程,基于点源函数基本理论,建立了Newton-非Newton双区复合水平井试井解释数学模型.利用Laplace积分变换和Fourier有限余弦积分变换方法,获得了Laplace空间Newton-非Newton双区复合水平井试井解释数学模型的解析解.通过Stehfest数值反演得到了典型无因次井底压力、压力导数特征曲线.研究表明:幂律指数越小,外区压力、压力导数曲线上翘越明显,且压力导数曲线呈斜率为(1-m)/(3-m)的直线;当幂律指数为1时,该模型简化为水平井常规双区复合模型;水平井水平段长度越长,早期径向流阶段结束的时间越早; 内外区流度比越大、 内区半径越小, 外区压力和压力导数曲线位置越高, 且始终保持斜率为(1-m)/(3-m)的直线. 相似文献
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F. Guillén-González 《Czechoslovak Mathematical Journal》2004,54(3):637-656
We study the system of PDEs describing unsteady flows of incompressible fluids with variable density and non-constant viscosity. Indeed, one considers a stress tensor being a nonlinear function of the symmetric velocity gradient, verifying the properties of p-coercivity and (p–1)-growth, for a given parameter p > 1. The existence of Dirichlet weak solutions was obtained in [2], in the cases p 12/5 if d = 3 or p 2 if d = 2, d being the dimension of the domain. In this paper, with help of some new estimates (which lead to point-wise convergence of the velocity gradient), we obtain the existence of space-periodic weak solutions for all p 2. In addition, we obtain regularity properties of weak solutions whenever p 20/9 (if d = 3) or p 2 (if d = 2). Further, some extensions of these results to more general stress tensors or to Dirichlet boundary conditions (with a Newtonian tensor large enough) are obtained. 相似文献
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非牛顿流体弹性径向渗流的自型问题的近似解 总被引:1,自引:0,他引:1
本文研究了非牛顿流体弹性径向渗流的自型解.设流体服从幂函数律.当指数n等于零时,文中得到了准确解.将此解和文献[1]的近似解作了比较.对于n>1及n<1的各种情形,文中得到了近似解.有算例. 相似文献
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S. I. Repin 《Journal of Mathematical Sciences》2004,123(6):4621-4636
The paper is concerned with estimates of deviations from exact solutions for stationary models of viscous incompressible fluids. It is shown that if a function compared with exact solution is subject to the incompressibility condition, then the deviation majorant consists of terms that penalize the inaccuracy in the equilibrium equation and the rheological relation defined by a ceratin dissipative potential. If such a function does not satisfy the incompressibility condition, then the majorant includes an additional term. The factor of this term depends on the constant in the Ladyzhenskaya–Babuka–Brezzi condition. Bibliography: 27 titles. 相似文献
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In this work we analyse a class of non-Newtonian reproductive fluid with a non-linear viscosity. The latter follows the power law or the Carreau's laws which is in common use for polymeric fluids. For a generalized data we introduce some special estimates and then obtain an existence result for the reproductive flow according to certain values of parameters appearing in the model. 相似文献
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Martin Fuchs 《Mathematical Methods in the Applied Sciences》1996,19(15):1225-1232
We discuss certain classes of quasi-static non-Newtonian fluids for which a power-law of the form σD=∇ϕ(ℰv) holds. Here σD is the stress deviator, v the velocity field, ℰv its symmetric derivative and ϕ is the function \[ \phi ({\cal E}v)=\frac 12\mu _\infty \left| {\cal E}v\right| ⁁2+\frac 1p\mu _0\left\{ \begin{array}{c} \left( 1+\left| {\cal E}v\right| ⁁2\right) ⁁{p/2} \\ \text{or} \\ \left| {\cal E}v\right| ⁁p \end{array} \right\}, \] ϕ(ℰv)=1 2 μ∞∣ℰv∣2+1 p μ0 (1+∣ℰv∣2)p/2 or ∣ℰv∣p, μ∞⩾0, μ0⩾0, μ∞+μ0>0, 1<p<∞. We then prove various regularity results for the velocity field v, for example differentiability almost everywhere and local boundedness of the tensor ℰv. 相似文献
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本文利用对非牛顿粘性不可压缩流方程对时间 t的解析性和长时间渐近性估计 ,具体构造了它的近似惯性流形 ,并得出收敛阶估计 . 相似文献
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Shu Wang & Fang Yuan 《偏微分方程(英文版)》2021,34(1):14-41
The aim of this paper is to explore the free boundary problem for the NonNewtonian shear thickening fluids. These fluids not only have vacuum, but also have
strong nonlinear properties. In this paper, a class of approximate solutions is first
constructed, and some uniform estimates are obtained for these approximate solutions.
Finally, the existence of free boundary problem solutions is proved by these uniform
estimates. 相似文献
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Hongjun Yuan & Huapeng Li 《偏微分方程(英文版)》2012,25(2):115-138
In this paper, we consider a class of non-Newtonian fluids in one-dimensional bounded interval. The global existence and uniqueness of solution are investigated. 相似文献