TY - JOUR T1 - Efficient Geometrical parametrization for finite-volume based reduced order methods JF - International Journal for Numerical Methods in Engineering Y1 - 2020 A1 - Giovanni Stabile A1 - Matteo Zancanaro A1 - Gianluigi Rozza AB -

In this work, we present an approach for the efficient treatment of parametrized geometries in the context of POD-Galerkin reduced order methods based on Finite Volume full order approximations. On the contrary to what is normally done in the framework of finite element reduced order methods, different geometries are not mapped to a common reference domain: the method relies on basis functions defined on an average deformed configuration and makes use of the Discrete Empirical Interpolation Method (D-EIM) to handle together non-affinity of the parametrization and non-linearities. In the first numerical example, different mesh motion strategies, based on a Laplacian smoothing technique and on a Radial Basis Function approach, are analyzed and compared on a heat transfer problem. Particular attention is devoted to the role of the non-orthogonal correction. In the second numerical example the methodology is tested on a geometrically parametrized incompressible Navier–Stokes problem. In this case, the reduced order model is constructed following the same segregated approach used at the full order level

VL - 121 UR - https://arxiv.org/abs/1901.06373 ER - TY - CONF T1 - The Effort of Increasing Reynolds Number in Projection-Based Reduced Order Methods: from Laminar to Turbulent Flows T2 - Lecture Notes in Computational Science and Engineering Y1 - 2020 A1 - Saddam Hijazi A1 - Shafqat Ali A1 - Giovanni Stabile A1 - F. Ballarin A1 - Gianluigi Rozza AB -

We present in this double contribution two different reduced order strategies for incompressible parameterized Navier-Stokes equations characterized by varying Reynolds numbers. The first strategy deals with low Reynolds number (laminar flow) and is based on a stabilized finite element method during the offline stage followed by a Galerkin projection on reduced basis spaces generated by a greedy algorithm. The second methodology is based on a full order finite volume discretization. The latter methodology will be used for flows with moderate to high Reynolds number characterized by turbulent patterns. For the treatment of the mentioned turbulent flows at the reduced order level, a new POD-Galerkin approach is proposed. The new approach takes into consideration the contribution of the eddy viscosity also during the online stage and is based on the use of interpolation. The two methodologies are tested on classic benchmark test cases.

JF - Lecture Notes in Computational Science and Engineering PB - Springer International Publishing CY - Cham SN - 978-3-030-30705-9 ER - TY - JOUR T1 - Enhancing CFD predictions in shape design problems by model and parameter space reduction JF - Advanced Modeling and Simulation in Engineering Sciences Y1 - 2020 A1 - Marco Tezzele A1 - Nicola Demo A1 - Giovanni Stabile A1 - Andrea Mola A1 - Gianluigi Rozza AB -

In this work we present an advanced computational pipeline for the approximation and prediction of the lift coefficient of a parametrized airfoil profile. The non-intrusive reduced order method is based on dynamic mode decomposition (DMD) and it is coupled with dynamic active subspaces (DyAS) to enhance the future state prediction of the target function and reduce the parameter space dimensionality. The pipeline is based on high-fidelity simulations carried out by the application of finite volume method for turbulent flows, and automatic mesh morphing through radial basis functions interpolation technique. The proposed pipeline is able to save 1/3 of the overall computational resources thanks to the application of DMD. Moreover exploiting DyAS and performing the regression on a lower dimensional space results in the reduction of the relative error in the approximation of the time-varying lift coefficient by a factor 2 with respect to using only the DMD.

VL - 7 UR - https://arxiv.org/abs/2001.05237 IS - 40 ER -