An efficient method of solving the Navier–Stokes equations for flow control

✍ Scribed by H. M. Park; M. W. Lee

• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 345 KB
• Volume: 41
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/(sici)1097-0207(19980330)41:6<1133::aid-nme329>3.0.co;2-y

✦ Synopsis

A new method of solving the Navier-Stokes equations e ciently by reducing their number of modes is proposed in the present paper. It is based on the Karhunen-Lo eve 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 su cient to describe the observed phenomena, and consequently reduce the Navier-Stokes equation deÿned on a complicated geometry to a set of ordinary di erential equations with a minimum degree of freedom. The present algorithm is well suited for the problems of ow control or optimization, where one has to compute the ow ÿeld repeatedly using the Navier-Stokes equation but one can also estimate the approximate solution space of the ow ÿeld based on the range of control variables. The low-dimensional dynamic model of viscous uid ow derived by the present method is shown to produce accurate ow ÿelds at a drastically reduced computational cost when compared with the ÿnite di erence solution of the Navier-Stokes equation.