ISSN:
0029-5981
Keywords:
flow control
;
numerical solution of Navier-Stokes equation
;
Karhunen-Loève Galerkin procedure
;
Engineering
;
Numerical Methods and Modeling
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
,
Technology
Notes:
A new method of solving the Navier-Stokes equations efficiently by reducing their number of modes is proposed in the present paper. It is based on the Karhunen-Loève decomposition which is a technique of obtaining empirical eigenfunctions from the experimental or numerical data of a system. Employing these empirical eigenfunctions as basis functions of a Galerkin procedure, one can a priori limit the function space considered to the smallest linear subspace that is sufficient to describe the observed phenomena, and consequently reduce the Navier-Stokes equation defined on a complicated geometry to a set of ordinary differential equations with a minimum degree of freedom. The present algorithm is well suited for the problems of flow control or optimization, where one has to compute the flow field repeatedly using the Navier-Stokes equation but one can also estimate the approximate solution space of the flow field based on the range of control variables. The low-dimensional dynamic model of viscous fluid flow derived by the present method is shown to produce accurate flow fields at a drastically reduced computational cost when compared with the finite difference solution of the Navier-Stokes equation. © 1998 John Wiley & Sons, Ltd.
Additional Material:
8 Ill.
Type of Medium:
Electronic Resource
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