In this work we provide a combination of isogeometric analysis with reduced order modelling techniques, based on proper orthogonal decomposition, to guarantee computational reduction for the numerical model, and with free-form deformation, for versatile geometrical parametrization. We apply it to computational fluid dynamics problems considering a Stokes flow model. The proposed reduced order model combines efficient shape deformation and accurate and stable velocity and pressure approximation for incompressible viscous flows, computed with a reduced order method. Efficient offine-online computational decomposition is guaranteed in view of repetitive calculations for parametric design and optimization problems. Numerical test cases show the efficiency and accuracy of the proposed reduced order model.

@article{SalmoiraghiBallarinHeltaiRozza2016,
title = {Isogeometric analysis-based reduced order modelling for incompressible linear viscous flows in parametrized shapes},
author = {Filippo Salmoiraghi and Francesco Ballarin and Luca Heltai and Gianluigi Rozza},
journal={Advanced Modeling and Simulation in Engineering Sciences},
year={2016},
volume={3},
number={1},
pages={21},
doi={10.1186/s40323-016-0076-6},
}