Unsteady two-dimensional flows in complex geometries: Comparative bifurcation studies with global eigenfunction expansions

被引:54
作者
Bangia, AK
Batcho, PF
Kevrekidis, IG
Karniadakis, GE
机构
[1] PRINCETON UNIV,PACM,PRINCETON,NJ 08544
[2] BROWN UNIV,PROVIDENCE,RI 02912
关键词
eigenfunction expansions; Galerkin method; bifurcation; continuation;
D O I
10.1137/S1064827595282246
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We present a bifurcation study of the incompressible Navier-Stokes equations in a model complex geometry: a spatially periodic array of cylinders in a channel. The dynamics of the how include a Hopf bifurcation from steady to oscillatory flow at an approximate Reynolds number R of 350 and the appearance of a second frequency at approximately R similar or equal to 890. The multiple frequency dynamics include a substantial increase in spatial and temporal scales with Reynolds number as compared with the simple limit cycle oscillation present close to R = 350. Numerical bifurcation studies of the dynamics are performed using three forms of global eigenfunction expansions. The first basis set is derived through principal factor analysis (Karhunen-Loeve expansion) of snapshots from accurate direct spectral element numerical solutions of the Navier-Stokes equations. The second set is obtained from the eigenfunctions of the Stokes operator for this geometry. Finally eigenfunctions are derived from a singular Stokes operator, i.e., the Stokes operator modified to include a Variable coefficient which vanishes at the domain boundaries. Truncated systems of (similar to 100) ODEs are obtained through projection of the Navier-Stokes equations onto the basis sets, and a comparative study of the resulting dynamical models is performed.
引用
收藏
页码:775 / 805
页数:31
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