CRPC-TR97703-S							November 1997

Title: Airfoil Design by an All-At-Once Method

Authors: Ajit Shenoy, Matthias Heinkenschloss, and Eugene M. Cliff

Submitted November 1997

Abstract:
The all-at-once approach is implemented to solve an optimum airfoil 
design problem. The airfoil design problem is formulated as a constrained 
optimization problem in which flow variables and design variables are 
viewed as independent and the coupling steady state Euler equation is 
included as a constraint, along with geometry and other constraints. In 
this formulation, the optimizer computes a sequence of points which tend 
toward feasiblility and optimality at the same time (all-at-once). This 
decoupling of variables typically makes the problem less nonlinear and 
can lead to more efficient solutions. In this paper an existing 
optimization algorithm is combined with an existing flow code. The 
problem formulation, its discretization, and the underlying solvers are 
described. Implementation issues are presented and numerical results are 
given which indicate that the cost of solving the design problem is 
approximately six times the cost of solving a single analysis problem.

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Ajit Shenoy
Interdisciplinary Center for Applied Mathematics and Aerospace Engg. Dept.
Virginia Polytechnic Institute and State University
Blacksburg, Virginia 24061-0531

Matthias Heinkenschloss
Department of Computational and Applied Mathematics
Rice University, Houston, Texas 77005-1892
heinken@caam.rice.edu

Eugene M. Cliff
Interdisciplinary Center for Applied Mathematics
and Aerospace Engg. Dept.
Virginia Polytechnic Institute and State University
Blacksburg, Virginia 24061-0531
cliff@icam.vt.edu