Shape optimization for the generalized Graetz problem

Shape optimization for the generalized Graetz problem

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Article ID: iaor2014893
Volume: 49
Issue: 6
Start Page Number: 993
End Page Number: 1008
Publication Date: Jun 2014
Journal: Structural and Multidisciplinary Optimization
Authors: , ,
Keywords: design
Abstract:

We apply shape optimization tools to the generalized Graetz problem which is a convection‐diffusion equation. The problem boils down to the optimization of generalized eigenvalues on a two phases domain. Shape sensitivity analysis is performed with respect to the evolution of the interface between the fluid and solid phase. In particular physical settings, counterexamples where there is no optimal domains are exhibited. Numerical examples of optimal domains with different physical parameters and constraints are presented. Two different numerical methods (level‐set and mesh‐morphing) are show‐cased and compared.

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