We consider the Boussinesq model of buoyancy driven fluid flows. This nonlinear system is solved numerically using a two level finite element method. On the first level, a nonlinear system is solved on a very coarse mesh. Thereafter, a linear system is solved on a fine mesh. In a standard approach, one might obtain the numerical solution from a discretization of the original, nonlinear system using the same fine mesh. Both solutions are of equal order of accuracy if the mesh widths are properly balanced. Therefore the two level method is very efficient. 相似文献
Single crystals of Al–0.1% Mn were channel-die compressed to a true strain of 2.3 and their recovery behaviour at 240–320°C investigated by microhardness measurements, electron backscatter diffraction (EBSD) microtexture mapping and X-ray line broadening analysis. The crystal orientations were the nominally stable Goss {110}?001?, brass {110}?112? and S {123}?634?. For all three orientations the microhardness decreases with a logarithmic time dependence but the instantaneous recovery rates of the brass oriented crystals are systematically lower than those of the other two orientations by a factor of about 2. The dislocation densities decrease rapidly in the first stages of recovery (<1?min) by dislocation dipole annihilation and more slowly thereafter. In the Goss and S orientations the later stage of recovery is due to sub-grain growth. The orientation dependence is ascribed to the relatively low misorientations developed by plastic straining in the brass crystals (average about 4°) compared with the Goss and S orientations (about 7–8°). 相似文献
Researches show that there exists a modal transformation matrix which is similar to that of the fixed interface method in form but slightly different from that in content. Using the constrained modes and normal modes or Lanczos vectors, a new modal transformation developed from hybrid method is given, in which the interface forces are replaced by interface displacements. The first synthesis equations are assembled easily as with the fixed interface method, yet the interface coordinates can be further eliminated as with the free-interface method. The new method unifies the fixed- and free-interface methods as well as hybrid method,permitting easy implementation of the Lanczos vectors to replace normal modes so that only static modes are calculated. The dynamic substructure method thus becomes more flexible and efficient. This reveals the interrelations of various dynamic substructure methods. New formula for modal analysis and modal synthesis are developed and three examples are given for illustration.Supported by Doctoral Training Foundation of State Education Commission and NNSF of China. 相似文献
Two β-aryl ether type model compounds, guaiacylglycol- and veratrylglycol-β-propylphenyl ethers, were copyrolyzed with borosilicate glass fibers. The results provided a better understanding of the effect of copyrolysis with the fibers on the yields of lignin-derived products from lignocellulosics.
The observed products indicated the following reactions occurring in the models; (1) cleavage of the C-aromatic ring bond, (2) cleavage of the β-ether bond, (3) cleavage of the C-Cβ bond, (4) ,β-dehydration, and (5) demethylation, and others. Of these reactions, reactions (1), (2) and (4) were the main pyrolysis reactions and fully explained the increase in the total yield of lignin-derived pyrolysis products from Japanese red pine (Pinus densiflora Sieb. et Zucc.) in the presence of borosilicate glass fibers. Reaction (1) was a particularly characteristic reaction in copyrolysis with the fibers. Important reactions relating to the increase in the total yield of lignin-derived pyrolysis products were reproduced on the models used. 相似文献