Cj. Wu et Hs. Shi, AN OPTIMAL THEORY FOR AN EXPANSION OF FLOW QUANTITIES TO CAPTURE THE FLOW STRUCTURES, Fluid dynamics research, 17(2), 1996, pp. 67-85
An optimal theory on how database analysis to capture the flow structu
res has been developed in this paper, which include the POD method as
its special case. By means of the remainder minimization method in the
Sobolev space, for more general optimal conditions the new theory has
the potential to overcome an inherent limitation of the POD method, i
.e., it cannot be used to the situations in which the optimal conditio
n is other than the inner product global one. As an example, using the
new theory, the database of a two-dimensional flow over a backward-fa
cing step is analyzed in detail, with velocity and vorticity bases.