POD and CVT-based reduced-order modeling of Navier-Stokes flows

被引:193
作者
Burkardt, John
Gunzburger, Max [1 ]
Lee, Hyung-Chun
机构
[1] Florida State Univ, Sch Computat Sci, Tallahassee, FL 32306 USA
[2] Ajou Univ, Dept Math, Suwon 442749, South Korea
关键词
reduced-order modeling; proper orthogonal decomposition; centroidal Voronoi tessellations; Navier-Stokes equations;
D O I
10.1016/j.cma.2006.04.004
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
A discussion of reduced-order modeling for complex systems such as fluid flows is given to provide a context for the construction and application of reduced-order bases. Reviews of the POD (proper orthogonal decomposition) and CVT (centroidal Voronoi tessellation) approaches to reduced-order modeling are provided, including descriptions of POD and CVT reduced-order bases, their construction from snapshot sets, and their application to the low-cost simulation of the Navier-Stokes system. Some concrete incompressible flow examples are used to illustrate the construction and use of POD and CVT reduced-order bases and to compare and contrast the two approaches to reduced-order modeling. (c) 2006 Elsevier B.V. All rights reserved.
引用
收藏
页码:337 / 355
页数:19
相关论文
共 54 条
[1]  
[Anonymous], PROPER ORTHOGONAL DE
[2]   PRESERVING SYMMETRIES IN THE PROPER ORTHOGONAL DECOMPOSITION [J].
AUBRY, N ;
LIAN, WY ;
TITI, ES .
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 1993, 14 (02) :483-505
[3]   THE PROPER ORTHOGONAL DECOMPOSITION IN THE ANALYSIS OF TURBULENT FLOWS [J].
BERKOOZ, G ;
HOLMES, P ;
LUMLEY, JL .
ANNUAL REVIEW OF FLUID MECHANICS, 1993, 25 :539-575
[4]   GALERKIN PROJECTIONS AND THE PROPER ORTHOGONAL DECOMPOSITION FOR EQUIVARIANT EQUATIONS [J].
BERKOOZ, G ;
TITI, ES .
PHYSICS LETTERS A, 1993, 174 (1-2) :94-102
[5]   Evaluation of proper orthogonal decomposition-based decomposition techniques applied to parameter-dependent nonturbulent flows [J].
Christensen, EA ;
Brons, M ;
Sorensen, JN .
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2000, 21 (04) :1419-1434
[6]   LOW-DIMENSIONAL MODELS FOR COMPLEX-GEOMETRY FLOWS - APPLICATION TO GROOVED CHANNELS AND CIRCULAR-CYLINDERS [J].
DEANE, AE ;
KEVREKIDIS, IG ;
KARNIADAKIS, GE ;
ORSZAG, SA .
PHYSICS OF FLUIDS A-FLUID DYNAMICS, 1991, 3 (10) :2337-2354
[7]   Voronoi-based finite volume methods, optimal Voronoi meshes, and PDEs on the sphere [J].
Du, Q ;
Gunzburger, MD ;
Ju, LL .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2003, 192 (35-36) :3933-3957
[8]   Constrained centroidal Voronoi tessellations for surfaces [J].
Du, Q ;
Gunzburger, MD ;
Ju, LL .
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2003, 24 (05) :1488-1506
[9]   Meshfree, probabilistic determination of point sets and support regions for meshless computing [J].
Du, Q ;
Gunzburger, M ;
Ju, LL .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2002, 191 (13-14) :1349-1366
[10]   Grid generation and optimization based on centroidal Voronoi tessellations [J].
Du, Q ;
Gunzburger, M .
APPLIED MATHEMATICS AND COMPUTATION, 2002, 133 (2-3) :591-607