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Analytic Hessian derivation for the quasi-one-dimensional Euler equations

✍ Scribed by Eyal Arian; Angelo Iollo

Publisher: Elsevier Science
Year: 2009
Tongue: English
Weight: 791 KB
Volume: 228
Category: Article
ISSN: 0021-9991
DOI: 10.1016/j.jcp.2008.09.021

No coin nor oath required. For personal study only.

✦ Synopsis

The Hessian for the quasi-one-dimensional Euler equations is derived. A pressure minimization problem and a pressure matching inverse problem are considered. The flow sensitivity, adjoint sensitivity, gradient and Hessian are calculated analytically using a direct approach that is specific to the model problems. For the pressure minimization problem we find that the Hessian exists and it contains elements with significantly larger values around the shock location. For the pressure matching inverse problem we find at least one case for which the gradient as well as the Hessian do not exist. In addition, two formulations for calculating the Hessian are proposed and implemented for the given problems. Both methods can be implemented in industrial applications such as large scale aerodynamic optimization.

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