In 1995, I prepared the following set of notes, based on my experiences with flow optimization using sensitivities. In this setting, we have some parameters that affect a fluid flow, and we have a scalar function based on properties of that flow. We want to find values of the parameters that optimize the scalar function, but the Navier Stokes equations are intermediate.
As a tool in these computations, we have available the flow sensitivities, which may be thought of as derivatives of flow components with respect to the parameters. These sensitivities can be interesting in their own right, particularly when the issue arises of whether sensitivities of the discretized variables are equivalent to discretizations of the sensitivities of the continuous variables.
In these notes, I also look at the question of a reduced basis, that is, the determination of a small set of vectors that seem to contain the most prominent directions of change for the physical parameters. If such a basis can be found effectively and efficiently, it may be possible to extend a known solution at a given parameter value by a good approximation that is valid over some reasonable range of the parameters.
A PDF version is available as ../../presentations/arby.pdf.
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