The upper sketch gives the geometric configuation for the target flow. The computed target flow is evaluated along the comparison plane, i.e., the computational exit plane.
The bottom sketch shows a body of half the length as that of the reference body. We would like the flow for the shorter body evaluated along the comparison plane to match as well as possible (in an L2 sense) the reference flow along the same plane.
To effect the matching of the second flow to the first, we can adjust the shape of the shortened body and the inflow Mach number. The shortened body is described by Bezier curves and we allow ourselves two free parameters. Thus, we have three parameters at our disposal to effect the matching: the inflow Mach number and two shape parameters.
Effect on the shortened body due to changes in the Bezier parameters
The initial flow used in the optimization
The target, initial, and optimal flows side-by-side