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Chaotic Lid-Driven Square Cavity Flows at Extreme Reynolds Numbers 被引量:1
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作者 Salvador Garcia 《Communications in Computational Physics》 SCIE 2014年第3期596-617,共22页
This paper investigates the chaotic lid-driven square cavity flows at extreme Reynolds numbers.Several observations have been made from this study.Firstly,at extreme Reynolds numbers two principles add at the genesis ... This paper investigates the chaotic lid-driven square cavity flows at extreme Reynolds numbers.Several observations have been made from this study.Firstly,at extreme Reynolds numbers two principles add at the genesis of tiny,loose counterclockwise-or clockwise-rotating eddies.One concerns the arousing of them owing to the influence of the clockwise-or counterclockwise currents nearby;the other,the arousing of counterclockwise-rotating eddies near attached to the moving(lid)top wall which moves from left to right.Secondly,unexpectedly,the kinetic energy soon reaches the qualitative temporal limit’s pace,fluctuating briskly,randomly inside the total kinetic energy range,fluctuations which concentrate on two distinct fragments:one on its upper side,the upper fragment,the other on its lower side,the lower fragment,switching briskly,randomly from each other;and further on many small fragments arousing randomly within both,switching briskly,randomly from one another.As the Reynolds number Re→∞,both distance and then close,and the kinetic energy fluctuates shorter and shorter at the upper fragment and longer and longer at the lower fragment,displaying tall high spikes which enlarge and then disappear.As the time t→∞(at the Reynolds number Re fixed)they recur from time to time with roughly the same amplitude.For the most part,at the upper fragment the leading eddy rotates clockwise,and at the lower fragment,in stark contrast,it rotates counterclockwise.At Re=109 the leading eddy-at its qualitative temporal limit’s pace—appears to rotate solely counterclockwise. 展开更多
关键词 Navier-Stokes equations lid-driven square cavity flows chaos
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FPn-Injective, FPn-Flat Covers and Preenvelopes, and Gorenstein AC-Flat Covers 被引量:13
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作者 Daniel Bravo Sergio Estrada Alina Iacob 《Algebra Colloquium》 SCIE CSCD 2018年第2期319-334,共16页
We prove that, for any n 〉 2, the classes of FPn-injective modules and of FPn-flat modules are both covering and preenveloping over any ring R. This includes the case of FP∞-injective and FP∞-flat modules (i.e., a... We prove that, for any n 〉 2, the classes of FPn-injective modules and of FPn-flat modules are both covering and preenveloping over any ring R. This includes the case of FP∞-injective and FP∞-flat modules (i.e., absolutely clean and, respectively, level modules). Then we consider a generalization of the class of (strongly) Gorenstein flat modules, i.e., the (strongly) Gorenstein AC-flat modules (cycles of exact complexes of flat modules that remain exact when tensored with any absolutely clean module). We prove that some of the properties of Gorenstein fiat modules extend to the class of Gorenstein AC-flat modules; for example, we show that this class is precovering over any ring R. We also show that (as in the case of Gorenstein flat modules) every Gorenstein AC-flat module is a direct summand of a strongly Gorenstein AC-flat module. When R is such that the class of Gorenstein AC-flat modules is closed under extensions, the converse is also true. Moreover, we prove that if the class of Gorenstein AC-flat modules is closed under extensions, then it is covering. 展开更多
关键词 FPn-injective module FPn-flat module Ding injective module GorensteinAC-flat module
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