TY - JOUR
T1 - Supremizer stabilization of POD-Galerkin approximation of parametrized Navier-Stokes equations
Y1 - 2015
A1 - Francesco Ballarin
A1 - Andrea Manzoni
A1 - Alfio Quarteroni
A1 - Gianluigi Rozza
AB - In this work, we present a stable proper orthogonal decompositionâ€“Galerkin approximation for parametrized steady incompressible Navierâ€“Stokes equations with low Reynolds number.
PB - Wiley
UR - http://urania.sissa.it/xmlui/handle/1963/34701
U1 - 34915
U2 - Mathematics
U4 - 1
U5 - MAT/08
ER -
TY - JOUR
T1 - Shape Optimization by Free-Form Deformation: Existence Results and Numerical Solution for Stokes Flows
Y1 - 2014
A1 - Francesco Ballarin
A1 - Andrea Manzoni
A1 - Gianluigi Rozza
A1 - Sandro Salsa
AB - Shape optimization problems governed by PDEs result from many applications in computational fluid dynamics. These problems usually entail very large computational costs and require also a suitable approach for representing and deforming efficiently the shape of the underlying geometry, as well as for computing the shape gradient of the cost functional to be minimized. Several approaches based on the displacement of a set of control points have been developed in the last decades, such as the so-called free-form deformations. In this paper we present a new theoretical result which allows to recast free-form deformations into the general class of perturbation of identity maps, and to guarantee the compactness of the set of admissible shapes. Moreover, we address both a general optimization framework based on the continuous shape gradient and a numerical procedure for solving efficiently three-dimensional optimal design problems. This framework is applied to the optimal design of immersed bodies in Stokes flows, for which we consider the numerical solution of a benchmark case study from literature.
PB - Springer
UR - http://urania.sissa.it/xmlui/handle/1963/34698
U1 - 34914
U2 - Mathematics
U4 - 1
ER -