AN OPTIMAL THEORY FOR AN EXPANSION OF FLOW QUANTITIES TO CAPTURE THE FLOW STRUCTURES

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.