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Shape optimization for viscous flows by reduced basis methods and free‐form deformation
Author(s) -
Manzoni Andrea,
Quarteroni Alfio,
Rozza Gianluigi
Publication year - 2011
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.2712
Subject(s) - discretization , shape optimization , basis (linear algebra) , mathematics , computation , reduction (mathematics) , mathematical optimization , parametrization (atmospheric modeling) , flow (mathematics) , navier–stokes equations , vorticity , computer science , geometry , algorithm , mathematical analysis , finite element method , mechanics , physics , quantum mechanics , vortex , compressibility , thermodynamics , radiative transfer
SUMMARY In this paper, we further develop an approach previously introduced in Lassila and Rozza, 2010, for shape optimization that combines a suitable low‐dimensional parametrization of the geometry (yielding a geometrical reduction) with reduced basis methods (yielding a reduction of computational complexity). More precisely, free‐form deformation techniques are considered for the geometry description and its parametrization, whereas reduced basis methods are used upon a FE discretization to solve systems of parametrized partial differential equations. This allows an efficient flow field computation and cost functional evaluation during the iterative optimization procedure, resulting in effective computational savings with respect to usual shape optimization strategies. This approach is very general and can be applied to a broad variety of problems. In this paper, we apply it to find the optimal shape of aorto‐coronaric bypass anastomoses based on vorticity minimization in the down‐field region. Blood flows in the coronary arteries are modeled using Stokes equations; afterwards, results have been verified in feedback using Navier–Stokes equations. Copyright © 2011 John Wiley & Sons, Ltd.