Open AccessA Continuous Adjoint Approach to Shape Optimization for Navier Stokes Flow
Author(s) -
Christian Brandenburg,
Florian Lindemann,
Michael Ulbrich,
Stefan Ulbrich
Publication year - 2009
Publication title -
international series of numerical mathematics
Language(s) - English
Resource type - Book series
eISSN - 2296-6072
pISSN - 0373-3149
DOI - 10.1007/978-3-7643-8923-9_2
Subject(s) - adjoint equation , computation , shape optimization , mathematics , navier–stokes equations , banach space , material derivative , flow (mathematics) , space (punctuation) , mathematical analysis , balanced flow , derivative (finance) , mathematical optimization , computer science , algorithm , geometry , finite element method , physics , partial differential equation , mechanics , compressibility , financial economics , economics , thermodynamics , operating system
In this paper we present an approach to shape optimization which is based on continuous adjoint computations. If the exact discrete adjoint equation is used, the resulting formula yields the exact discrete reduced gradient. We first introduce the adjoint-based shape derivative computation in a Banach space setting. This method is then applied to the instationary Navier-Stokes equations. Finally, we give some numerical results.
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