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91.
Z. Skalk 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2011,91(9):724-732
Let Ω ⊆ ℝ3 be a uniformly regular domain of the class C3 or Ω = ℝ3. Let A denote the Stokes operator and {Eλ; λ > 0} be the resolution of identity of A. We show as the main result of the paper that if w is a nonzero global weak solution to the Navier‐Stokes equations in Ω satisfying the strong energy inequality, then there exists a nonnegative finite number a = a(w) such that for every ε > 0 [lim_{t rightarrow infty} frac {||(E_{a+varepsilon}‐E_{a‐varepsilon}) w(t)||} {||w(t)||} = 1, ] where we put Ea‐ε = 0 if a‐ε < 0. Thus, every nonzero global weak solution satisfying the strong energy inequality exhibits large‐time energy concentration in a particular frequency. Moreover, the solutions with the exponentially decreasing energy are characterized by the positivity of a. In Appendix, we present some further results describing in detail the large‐time behavior of w. 相似文献
92.
In this paper, the 3D Navier–Stokes (N–S) equation and Cahn–Hilliard (C–H) equations were solved using a free‐energy‐based lattice Boltzmann (LB) model. In this model, a LB equation with a D3Q19 velocity model is used to recover continuity and N–S equations while another LB equation with D3Q7 velocity model for solving C–H equation (Int. J. Numer. Meth. Fluids, 2008; 56 :1653–1671) is applied to solve the 3D C–H equation. To avoid the excessive use of computational resources, a moving reference frame is adopted to allow long‐time simulation of a bubble rising. How to handle the inlet/outlet and moving‐wall boundary conditions are suggested. These boundary conditions are simple and easy for implementation. This model's performance on two‐phase flows was investigated and the mass conservation of this model was evaluated. The model is validated by its application to simulate the 3D air bubble rising in viscous liquid (density ratio is 1000). Good agreement was obtained between the present numerical results and experimental results when Re is small. However, for high‐Re cases, the mass conservation seems not so good as the low‐Re case. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
93.
基于有限元方法的思想, 给出了厚度线性变化的薄壁结构扇性几何性质计算的一种方法, 通过数值实施, 表明了所给方法的正确和有效性. 相似文献
94.
超晶格材料是由两种或两种以上性质不同的薄膜交替生长而形成的人工周期性结构材料.超晶格材料中具有连续介质力学``小尺度效应'和量子力学``大尺寸量子效应'并存的现象.阐述了超晶格材料周期结构特征和制备技术,介绍了超晶格材料量子化能带结构及其奇异的光电特性.探讨了超晶格材料微观结构及其变形机理,归纳了超晶格材料量子化电子结构的几种常用计算方法,如紧束缚方法、赝势方法和k$ cdot $p微扰方法等.重点介绍了外力场和应变对超晶格材料量子化电子结构及其光电性质影响,包括作者所在研究小组近期在端部摩擦、点载荷、有限界面和各向异性等对超晶格微观变形及其量子化电子结构影响的跨尺度一体化研究方面的最新工作进展. 相似文献
95.
Modes obtained using the Proper Orthogonal Decomposition are used as boundary enrichment functions within a variational multiscale method for the stochastically forced Burgers equation. Initially, large increases in accuracy are obtained using the enrichment functions without stabilisation terms. Then, optimal coefficients for the stabilisation parameter τ of the unresolved scale model are calibrated using a goal‐oriented model‐constrained optimisation technique, resulting in further improvements. As both the determination of the enrichment functions and the optimisation of the coefficients requires high‐accuracy reference data, a scaling procedure is introduced to allow their use over range of conditions. Numerical experiments confirm that the scaling procedure is effective. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
96.
A volume-filtered Euler–Lagrange large eddy simulation methodology is used to predict the physics of turbulent liquid–solid slurry flow through a horizontal periodic pipe. A dynamic Smagorinsky model based on Lagrangian averaging is employed to account for the sub-filter scale effects in the liquid phase. A fully conservative immersed boundary method is used to account for the pipe geometry on a uniform cartesian grid. The liquid and solid phases are coupled through volume fraction and momentum exchange terms. Particle–particle and particle–wall collisions are modeled using a soft-sphere approach. Three simulations are performed by varying the superficial liquid velocity to be consistent with the experimental data by Dahl et al. (2003). Depending on the liquid flow rate, a particle bed can form and develop different patterns, which are discussed in light of regime diagrams proposed in the literature. The fluctuation in the height of the liquid-bed interface is characterized to understand the space and time evolution of these patterns. Statistics of engineering interest such as mean velocity, mean concentration, and mean streamwise pressure gradient driving the flow are extracted from the numerical simulations and presented. Sand hold-up calculated from the simulation results suggest that this computational strategy is capable of predicting critical deposition velocity. 相似文献
97.
In this paper I review a coarse-grained fluid theory named the finite scale theory and describe the development of its numerical analog, implicit large eddy simulation (ILES). The derivation, interpretation and properties of the finite scale equations are discussed and connections to other physical theory and numerical methods are elucidated. 相似文献
98.
O.T. Bruhns 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2014,94(3):187-202
At the beginning of the last century two different types of constitutive relations to describe the complex behavior of elasto‐plastic material were presented. These were the deformation theory originally developed by Hencky and the Prandtl‐Reuss theory. Whereas the former provides a direct solid‐like relation of stress as function of strain, the latter has been based on an additive composition of elastic and plastic parts of the increments of strains. These in turn were taken as a solid‐ and fluid‐like combination of the de Saint‐Venant/Lévy theory with an incremental form of Hooke's law. Even nowadays this Prandtl‐Reuss theory is still accepted – within the restriction of small elastic deformations, i.e. it is generally stated in most textbooks on plasticity that this theory due to a number of defects can not be applied to large deformations. In the present article it is shown that this restrictive statement may be no longer true. Introducing a specific objective time derivative it could be shown that these defects disappear. 相似文献
99.
A multiphase flow model has been established based on a moving particle semi‐implicit method. A surface tension model is introduced to the particle method to improve the numerical accuracy and stability. Several computational techniques are employed to simplify the numerical procedure and further improve the accuracy. A particle fraction multiphase flow model is developed and verified by a two‐phase Poiseuille flow. The multiphase surface tension model is discussed in detail, and an ethanol drop case is introduced to verify the surface tension model. A simple dam break is simulated to demonstrate the improvements with various modifications in particle method along with a new boundary condition. Finally, we simulate several bubble rising cases to show the capacity of this new model in simulating gas–liquid multiphase flow with large density ratio difference between phases. The comparisons among numerical results of mesh‐based model, experimental data, and the present model, indicate that the new multiphase particle method is acceptable in gas–liquid multiphase fluids simulation. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
100.
This paper attempts to reproduce numerically previous experimental findings with opposed flows and extends their range to quantify the effects of upstream pipes and nozzles with inviscid, laminar and turbulent flows. The choice of conservation equations, boundary conditions, algorithms for their solution, the degree of grid dependence, numerical diffusion and the validity of numerical approximations are justified with supporting calculations where necessary. The results of all calculations on the stagnation plane show maximum strain rates close to the annular exit from the nozzles and pipes for lower separations and it can be expected that corresponding reacting flows will tend to extinguish in this region with the extinction moving towards the axis. With laminar flows, the maximum strain rate increased with Reynolds number and the maximum values were generally greater than with inviscid flows and smaller than with turbulent flows. With large separations, the strain rates varied less and this explains some results with reacting flows where the extinction appeared to begin on the axis. The turbulent‐flow calculations allowed comparison of three common variants of a two‐equation first‐moment closure. They provided reasonable and useful indications of strain rates but none correctly represented the rms of velocity fluctuations on the axis and close to the stagnation plane. As expected, those designed to deal with this problem produced results in better agreement with experiment but were still imperfect. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献