It is said that one can reduce the time and cost of computation by use of reduced-order models. While when we reconstruct the flow field, the initial data from the numerical simulation or experiments are still needed. It seems that it doesn't reduce the data storage. Thanks.

I'm not quite sure what you mean by data storage. While it is true that to construct a POD reduced order model simulation data from the original full model must be computed at least once, from then on the reduced system is much smaller and computation can be made much faster..

I am sorry I don't know much about the POD, but what kind of computation can be made much faster?

The speed of computation is more or less based on the number of DOF to be solved for. POD reduces this number...therefore the computation is sped up. It has been applied to aerodynamic and aeroelastic computations which used vortex lattice,Euler and Navier Stokes fluid equations. Look for the authors Dowell,Hall and Thomas for references.

Ignoreance is bliss!!, but what is POD? Can someone explain it?

check out:

G Berkooz, P Holmes, and JL Lumley. "The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows", Annu. Rev. Fluid Mech. 1993 , Vol. 25: 539-575.

Proper Orthogonal Decomposition. Essentially it is a coordinate transformation which maps the flow variables(for example pressure,velocity,density) from a large dimension subspace to a smaller dimension subspace via the coordinate transform. It is of the same thought as what is done with structural dynamics where the structural deformation can be thought of as a linear combination of some global modes...for the fluid simulation the pressure etc can be described by a reduced set of bases. The bases("modes") are found by solving the eigenvalue problem [C]{v}=lamda{v} where C is the correlation matrix formed by putting snapshots of the original full model data into a matrix(call it Q) a forming the correlation C=Q*Q^T. The POD modes are then formed via [U]=[Q][V] See the reference I gave above for more(better) detail.