Shape optimization for viscous flows by reduced basis methods and free-form deformation

31/2010

Shape optimization for viscous flows by reduced basis methods and free-form deformation

Saturday 6th November 2010

Manzoni, Andrea; Quarteroni, Alfio; Rozza, Gianluigi

In this paper we present a new approach for shape optimization that combines two different types of model reduction: a suitable low-dimensional parametrization of the geometry (yielding a geometrical reduction) combined with reduced basis methods (yielding a reduction of computational complexity). More precisely, free-form deformation techniques are introduced for the geometry description and its parametrization, while reduced basis methods are used upon a finite element 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 for a broad variety of problems. To prove its effectivity, 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. Stokes equations are used to model blood flow in the coronary arteries.