RESUMO
The proper orthogonai decomposition (POD) method for the instatiouary Navier-Stokes equations is considered. Several numerical approaches to evaluating the POD eigenfunctions are presented. The POD eigenfunctions are applied as a basis for a Galerkin projection of the instationary Navier-Stokes equations. And a low-dimensional ordinary differential models for fluid flows governed by the instationary Navier-Stokes equations are constructed. The numerical examples show that the method is feasible and efficient for optimal control of fluids.
RESUMO
The proper orthogonal decomposition (POD) method for the instationary Navier-Stokes equations is considered. Several numerical approaches to evaluating the POD eigenfunctions are presented. The POD eigenfunctions are applied as a basis for a Galerkin projection of the instationary Navier-Stokes equations. And a low-dimensional ordinary differential models for fluid flows governed by the instationary Navier-Stokes equations are constructed. The numerical examples show that the method is feasible and efficient for optimal control of fluids.
RESUMO
Two inequalities in the book Navier-Stokes Equations Theory and Numerical Analysis written by Roger Temam are improved via Schwarz's inequality and Young's inequality, and the coefficients of them are simplified from 21/4·31/2 and 21/2·33/4 to 21/4 and 23/4, respectively. Therefore, to some extent the approximating error can be reduced and the accuracy of approximation can be improved.