PRESERVING SYMMETRIES IN THE PROPER ORTHOGONAL DECOMPOSITION

被引:98
作者
AUBRY, N
LIAN, WY
TITI, ES
机构
[1] UNIV CALIF IRVINE,DEPT MATH,IRVINE,CA 92717
[2] CUNY CITY COLL,DEPT MECH ENGN,NEW YORK,NY 10031
[3] CORNELL UNIV,CTR APPL MATH,ITHACA,NY 14853
关键词
PROPER ORTHOGONAL DECOMPOSITION; KARHUNEN-LOEVE EXPANSION; EMPIRICAL EIGENFUNCTIONS; KURAMOTO-SIVASHINSKY EQUATION;
D O I
10.1137/0914030
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The proper orthogonal decomposition (POD) (also called Karhunen-Loeve expansion) has been recently used in turbulence to derive optimally fast converging bases of spatial functions, leading to efficient finite truncations. Whether a finite number of these modes can be used in numerical simulations to derive an ''accurate'' finite set of ordinary differential equations, over a certain range of bifurcation parameter values, still remains an open question. It is shown here that a necessary condition for achieving this goal is that the truncated system inherit the symmetry properties of the original infinite-dimensional system. In most cases, this leads to a systematic involvement of the symmetry group in deriving a new expansion basis called the symmetric POD basis. The Kuramoto-Sivashinsky equation with periodic boundary conditions is used as a paradigm to illustrate this point of view. However, the conclusion is general and can be applied to other equations, such as the Navier-Stokes equations, the complex Ginzburg-Landau equation, and others.
引用
收藏
页码:483 / 505
页数:23
相关论文
共 68 条
[1]  
[Anonymous], INFINITE DIMENSIONAL
[2]   KURAMOTO-SIVASHINSKY DYNAMICS ON THE CENTER-UNSTABLE MANIFOLD [J].
ARMBRUSTER, D ;
GUCKENHEIMER, J ;
HOLMES, P .
SIAM JOURNAL ON APPLIED MATHEMATICS, 1989, 49 (03) :676-691
[3]   SPATIOTEMPORAL ANALYSIS OF COMPLEX SIGNALS - THEORY AND APPLICATIONS [J].
AUBRY, N ;
GUYONNET, R ;
LIMA, R .
JOURNAL OF STATISTICAL PHYSICS, 1991, 64 (3-4) :683-739
[4]   THE DYNAMICS OF COHERENT STRUCTURES IN THE WALL REGION OF A TURBULENT BOUNDARY-LAYER [J].
AUBRY, N ;
HOLMES, P ;
LUMLEY, JL ;
STONE, E .
JOURNAL OF FLUID MECHANICS, 1988, 192 :115-173
[5]  
Aubry N., 1991, Theoretical and Computational Fluid Dynamics, V2, P339, DOI 10.1007/BF00271473
[6]  
AUBRY N, UNPUB PHYS FLUIDS A
[7]  
AUBRY N, 1991, 9106019 U NEW YORK C
[8]  
AUBRY N, 1992, NONLINEAR SCI, V2, P183
[9]  
AUBRY N, 1991, 1989 P GREN FRANC C, P227
[10]   VISCOUS SUBLAYER AND ADJACENT WALL REGION IN TURBULENT PIPE FLOW [J].
BAKEWELL, HP ;
LUMLEY, JL .
PHYSICS OF FLUIDS, 1967, 10 (9P1) :1880-&