《Table 2 The accumulative e ne rgy of the proje ction of fluctuating ve locity fie ld on the first N

《Table 2 The accumulative e ne rgy of the proje ction of fluctuating ve locity fie ld on the first N   提示:宽带有限、当前游客访问压缩模式
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《POD Analysis and Low-Dimensional Model Based on POD-Galerkin for Two-Dimensional Rayleigh-Bénard Convection》


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We approximated the POD eigenfunctions(or eigenmodes)using 200 snapshots.The relative contribution of each POD eigenmode is displayed in Fig.3.From Fig.3,it clearly show s that the fluctuating energy in the first eigenmodes is larger,how ever,high-order eigenmodes contains small fluctuating energy and the distribution is uniform.Table 2 lists the accumulative energy of the fluctuating velocity for first several eigenmodes.It is can be found that the first eigenmode contains(on average)23.94%of the fluctuating energy.Coherent structures are seen as the sum of several eigenmodes that possess a dominant energy of the flow over 90%.From Table 2,w e can find that the demanded numbers of eigenmodes is 10.So from the theory,it is sufficient to construct the LDM for RB convection using only 10 eigenmodes,w hich can reflect the original flow system.For a comparison,w e also choose 30 and 50 eigenmodes to build LDM.The results w ill be discussed in Sections4.2.