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Intrusive and non-intrusive reduced order methods for parametric problems using OpenFoam

Despite the recent increase of the available computational power in many occasions standard discretization techniques (Finite Volumes, Finite Elements, Finite Differences, etc..) are not a viable approach. Such a condition occurs in the context of parametric problems when a large number of system configurations are in need of being tested or a reduced computational time is required. A typical example of such situations can be found for example in uncertainty quantification, shape optimization, inverse problems, or real-time control. Reduced order models [1] demonstrated to offer a possible approach to reduce the computational time required to evaluate a new solution in the parameter space. In this talk, I will present several reduced order modeling techniques for parametrized problems implemented using ITHACA-FV, an in-house open source c++ library based on OpenFOAM, and other python-based open-source packages (https://mathlab.sissa.it/cse-software). I will discuss different types of reduced order models of both the intrusive and non-intrusive types such as the Proper Orthogonal Decomposition (POD)-Galerkin approach, the POD with interpolation, the Dynamic Mode Decomposition (DMD). Both physical and geometrical parametrization will be discussed. Particular attention will be devoted to geometrically parametrized problems [2] and to the different techniques that can be used to efficiently morph the computational domain. The developed methodology will be presented on computational fluid dynamics problems for both stationary and non-stationary cases.

[1] Chinesta, F., Huerta, A., Rozza, G. and Willcox, K. (2017). Model Reduction Methods. In Encyclopedia of Computational Mechanics Second Edition (eds E. Stein, R. Borst and T.J.R. Hughes). doi:10.1002/9781119176817.ecm2110

[2] Stabile, G., Zancanaro M. and Rozza G. (2020). Efficient Geometrical parametrization for finite-volume based reduced order methods, Int J Numer Methods Eng. 2020; 1– 28. https://doi.org/10.1002/nme.6324