Efficient Numerical Multilevel Methods for the Optimization of Gas Turbine Combustion Chambers

  • S. Ulbrich
  • R. RothEmail author
Part of the Fluid Mechanics and Its Applications book series (FMIA, volume 1581)


In this paper we present an approach for the optimization of turbulent flows. To accomplish such a complex task, the general strategy has to be carefully designed. On the optimization side, we incorporate multilevel optimization algorithms. With this kind of algorithms, different levels describing a problem can be efficiently used for the optimization. Typical examples are discretization levels or models of different physical fidelity. Many optimization algorithms rely on gradient information, which is generally not available for complex problems described by partial differential equations (PDEs). Nevertheless, gradient information can be obtained from computer programs by the use of Automatic Differentiation (AD) techniques. We present a discrete adjoint approach, which was applied to the flow solver FASTEST. The numerical results show the efficiency of the adjoint mode and the optimization algorithms. They include shape optimization and boundary control examples for the Navier-Stokes Equations (NSE), Large Eddy Simulation (LES) and Reynolds Averaged Navier-Stokes (RANS) Equations.


Discrete Adjoint Optimal Control Multilevel Optimization Shape Optimization 



The authors gratefully acknowledge the support of the Sonderforschungbereich 568 funded by the German Research Foundation (DFG). Moreover, the first author was supported by the Graduate School Computational Engineering and the Center of Smart Interfaces at TU Darmstadt, which are both funded by the German Research Foundation (DFG).


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Nonlinear Optimization, Department of MathematicsTechnische Universität DarmstadtDarmstadtGermany

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