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41.
Decoupled two‐grid finite element method for the time‐dependent natural convection problem I: Spatial discretization 下载免费PDF全文
Tong Zhang JinYun Yuan ZhiYong Si 《Numerical Methods for Partial Differential Equations》2015,31(6):2135-2168
In this article, a decoupled two grid finite element method (FEM) is proposed and analyzed for the nonsteady natural convection problem using the coarse grid numerical solutions to decouple the nonlinear coupled terms, and the corresponding optimal error estimates are derived. Compared with the standard Galerkin FEM and the usual two‐grid FEM, our algorithm not only keeps good accuracy but also saves a lot of computational cost. Some numerical examples are provided to verify the performances of the decoupled two‐grid FEM. Both theoretical analysis and numerical experiments show the efficiency and effectiveness of the decoupled two‐grid FEM for the nonsteady natural convection problem. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 2135–2168, 2015 相似文献
42.
S. V. Nizhankovskyi A. V. Tan'ko N. S. Sidelnikova G. T. Adonkin 《Crystal Research and Technology》2015,50(3):223-229
It is shown that the formation of longitudinal aggregation of inclusions in bulk sapphire and yttrium‐aluminum garnet (YAG) grown by the method of HDC is caused by local accumulation of impurities, disturbance of morphological stability of the crystallization front and capture of inclusions and impurities in the nodal region of the melt two‐vortex convection. Studied is the influence of thermal and geometrical parameters of the melt and the shape of the crystallization front on the conditions of the formation of the capture of inclusions. 相似文献
43.
A high‐order convection‐bounded scheme is constructed by combining the total variational diminishing constraint and convection boundedness criterion condition in the normalized variable formulation. It employs the Hermite polynomial interpolation to design its characteristic line in the normalized variable diagram. Numerical results of the convection‐dominated problems with smooth or discontinuous initial distributions demonstrate the present scheme possesses high resolution and good robustness. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
44.
A numerical investigation of the mixed convection heat transfer from vertical helically coiled tubes in a cylindrical shell at various Reynolds and Rayleigh numbers, various coil‐to‐tube diameter ratios and non‐dimensional coil pitches was carried out. The particular difference in this study compared with other similar studies is the boundary conditions for the helical coil. Most studies focus on constant wall temperature or constant heat flux, whereas in this study it was a fluid‐to‐fluid heat exchanger. The purpose of this article is to assess the influence of the tube diameter, coil pitch and shell‐side mass flow rate on shell‐side heat transfer coefficient of the heat exchanger. Different characteristic lengths were used in the Nusselt number calculations to determine which length best fits the data and finally it has been shown that the normalized length of the shell‐side of the heat exchanger reasonably demonstrates the desired relation. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
45.
A semi-implicit multi-layer spherical spectral method for simulating stellar core convection is described. The fully compressible three-dimensional hydrodynamic equations with rotation and energy generation are solved. Prognostic variables are expressed as finite sums of spherical harmonics in the horizontal directions and handled by the finite difference method in the radial direction. The stratified approximation is used to simplify the nonlinearity to quadratic. A multi-layer scheme is employed to overcome the time step problem arising from shrinking grid sizes in the physical space near the center of the star. Despite of the different spectral truncations in different layers, round-off conservation of the total mass and total angular momentum of the whole domain can be maintained, and were confirmed numerically. The code is parallelized; with 12 processors the speedup factor is about 9. The solutions of model core convection with and without rotation are discussed. 相似文献
46.
Infinite Prandtl Number Convection 总被引:1,自引:0,他引:1
We prove an inequality of the type NCR
1/3(1+log+
R)2/3 for the Nusselt number N in terms of the Rayleigh number R for the equations describing three-dimensional Rayleigh–Bénard convection in the limit of infinite Prandtl number. 相似文献
47.
48.
We analyze the effective diffusivity of a passive scalar in a two-dimensional, steady, incompressible random flow that has
mean zero and a stationary stream function. We show that in the limit of small diffusivity or large Peclet number, with convection
dominating, there is substantial enhancement of the effective diffusivity. Our analysis is based on some new variational principles
for convection diffusion problems and on some facts from continuum percolation theory, some of which are widely believed to
be correct but have not been proved yet. We show in detail how the variational principles convert information about the geometry
of the level lines of the random stream function into properties of the effective diffusivity and substantiate the result
of Isichenko and Kalda that the effective diffusivity behaves likeɛ
3/13 when the molecular diffusivityɛ is small, assuming some percolation-theoretic facts. We also analyze the effective diffusivity for a special class of convective
flows, random cellular flows, where the facts from percolation theory are well established and their use in the variational
principles is more direct than for general random flows. 相似文献
49.
Cerisier P Porterie B Kaiss A Cordonnier J 《The European physical journal. E, Soft matter》2005,18(1):85-93
The motion of particles moving under gravity in the velocity field of a liquid in a Bénard hexagonal cell is studied experimentally
and numerically for Stokes flow conditions. We then explain the settlement of particles in the centers of cells to form a
regular quincunx. It is found that sedimentation also occurs preferentially along the lines connecting the centers of adjacent
cells to form a triangle deposition tessellation. Finally, it is explained why particles occupy the central part of each convective
cell while the peripheral part of the cell quickly becomes limpid. Numerical results are in agreement with the experimental
observations of Bénard and those of the present study. 相似文献
50.