Mathematics

We present a new pipeline for the Model Order Reduction, from the geometrical parametriza-tion to the construction of the reduced basis, for complex engineering problems. The pro-posed approach relies on Free Form Deformation (FFD) for the geometrical parametrization,a "leave one out" strategy for the selection of the parameters value and Proper OrthogonalDecomposition (POD) with interpolation of the POD coefficients for the online evaluation.Since most of the time engineers are interested in the outputs of a problem instead of thewhole solution, both the parameters selection and reduced basis construction are performeddirectly on the output of interest. After a general presentation of the pipeline, we show theapplication to the solution of steady RANS equations around drivAer model with paramet-ric bumper shape. The outputs of interest are the pressure and wall stress fields on the car,which are fundamental for the computation of drag and lift coefficients. The results showa speed-up of order of millions with an error of about 4%. Alongside we briefly present twonew Python libraries developed at SISSA mathLab for model order reduction, namelyPyGeM and EZyRB. http://mathlab.sissa.it/cse-software