A continuous adjoint formulation for the computation of topological and surface sensitivities of ducted flows

Topology optimization of fluid dynamic systems is a comparatively young optimal design technique. Its central ingredient is the computation of topological sensitivity maps. Whereas, for finite element solvers, implementations of such sensitivity maps have been accomplished in the past, this study focuses on providing this functionality within a professional finite volume computational fluid dynamics solver. On the basis of a continuous adjoint formulation, we derive the adjoint equations and the boundary conditions for typical cost functions of ducted flows and present first results for two‐ and three‐dimensional geometries. Emphasis is placed on the versatility of our approach with respect to changes in the objective function. We further demonstrate that surface sensitivity maps can also be computed with the implemented functionality and establish their connection with topological sensitivities. Copyright © 2008 John Wiley & Sons, Ltd.

[1]  K. Svanberg.  The method of moving asymptotes—a new method for structural optimization , 1987 .

[2]  A. Jameson,et al.  A COMPARISON OF THE CONTINUOUS AND DISCRETE ADJOINT APPROACH TO AUTOMATIC AERODYNAMIC OPTIMIZATION , 2000 .

[3]  Niles A. Pierce,et al.  An Introduction to the Adjoint Approach to Design , 2000 .

[4]  J. Samareh.  Survey of Shape Parameterization Techniques for High-Fidelity Multidisciplinary Shape Optimization , 2001 .

[5]  Juan G. Santiago,et al.  Incomplete sensitivities in design and control of fluidic channels , 2001 .

[6]  Rainald Löhner,et al.  A stabilized pseudo-shell approach for surface parametrization in CFD design problems , 2002 .

[7]  Rainald Löhner,et al.  An Adjoint-Based Design Methodology for CFD Optimization Problems , 2003 .

[8]  J. Petersson,et al.  Topology optimization of fluids in Stokes flow , 2003 .

[9]  OPTIMIZATION OF NAVIER-STOKES FLOW IN MICROFLUIDICS , 2004 .

[10]  Rainald Löhner,et al.  On the Boundary Computation of Flow Sensitivities , 2004 .

[11]  Jens-Dominik Müller,et al.  On the performance of discrete adjoint CFD codes using automatic differentiation , 2005 .

[12]  O. Sigmund,et al.  Topology optimization of channel flow problems , 2005 .

[13]  L. H. Olesen,et al.  A high‐level programming‐language implementation of topology optimization applied to steady‐state Navier–Stokes flow , 2004, physics/0410086.

[14]  R. Giering,et al.  Computation of topological sensitivities in fluid dynamics: Cost function versatility , 2006 .

[15]  James K. Guest,et al.  Topology optimization of creeping fluid flows using a Darcy–Stokes finite element , 2006 .

[16]  R. Dwight,et al.  Eect of Various Approximations of the Discrete Adjoint on Gradient-Based Optimization , 2006 .

[17]  S. Mittal,et al.  A stabilized finite element method for shape optimization in low Reynolds number flows , 2007 .

[18]  C. Othmer,et al.  Implementation of a continuous adjoint for topology optimization of ducted flows , 2007 .

[19]  Cecil Armstrong,et al.  Linking Adjoint Sensitivity Maps with CAD Parameters , 2008 .