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: | Gournay Frdric, Fehrenbach Jrme, Plourabou Franck |
Keywords: | design |
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.