On the Optimality System for a 1-D Euler Flow Problems
Eugene M. Cliff
Aerospace and Ocean Engineering Deptartment
Virginia Polytechnic Institute and State University
Matthias Heinkenschloss
Department of Computational and Applied Mathematics
Rice University
Ajit R. Shenoy
Aerospace and Ocean Engineering Deptartment
Virginia Polytechnic Institute and State University
AIAA Paper 96-3993, September 1996
Abstract
In this paper, a problem of shape design for a duct with the flow
governed by the one-dimensional Euler equations is analyzed.
The flow is assumed to be transonic, in the sense that we have a shock
embedded in the flow. The presence of the shock introduces analytical
and numerical difficulties that are overcome by introducing the shock location
as an explicit state variable. We justify the use of adjoint
variables by establishing conditions to ensure that
the linearized constraint is surjective. These adjoint variables are
used to state necessary optimality conditions and to compute
gradients. In addition, our characterization of the adjoint variables
is of interest for comparison to adjoints associated
with shock-capturing formulations.
Keywords
Euler flow equations, adjoint equations, optimal control.
PDF file (117kB)