A parametric Reduced Order Model (ROM) for buoyancy-driven flow is developed for which the Full Order Model (FOM) is based on the finite volume approximation and the Boussinesq approximation is used for modeling the buoyancy. Therefore, there exists a two-way coupling between the incompressible Boussinesq equations and the energy equation. The reduced basis is constructed with a Proper Orthogonal Decomposition (POD) approach and to obtain the Reduced Order Model, a Galerkin projection of the governing equations onto the reduced basis is performed. The ROM is tested on a 2D differentially heated cavity of which the side wall temperatures are parametrized. The parametrization is done using a control function method. The aim of the method is to obtain homogeneous POD basis functions. The control functions are obtained solving a Laplacian function for temperature. Only one full order solution was required for the reduced basis creation. The obtained ROM is stable for different parameter sets for which the temperature difference between the walls is smaller than for the set in the FOM used for the POD basis creation. Then, the relative error between the FOM and the ROM for temperature is below 10−4 and for velocity below 10−1 for the vast part of the simulation time. Finally, the ROM is about 20 times faster than the FOM run on a single processor.

Pod-Galerkin reduced order model of the Boussinesq approximation for buoyancy-driven enclosed flows / Star, K.; Stabile, G.; Georgaka, S.; Belloni, F.; Rozza, G.; Degroote, J.. - (2019), pp. 2452-2461. ((Intervento presentato al convegno 2019 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019 tenutosi a Portland Marriott Downtown Waterfront, USA nel 2019.

Pod-Galerkin reduced order model of the Boussinesq approximation for buoyancy-driven enclosed flows

Stabile G.;Rozza G.;
2019-01-01

Abstract

A parametric Reduced Order Model (ROM) for buoyancy-driven flow is developed for which the Full Order Model (FOM) is based on the finite volume approximation and the Boussinesq approximation is used for modeling the buoyancy. Therefore, there exists a two-way coupling between the incompressible Boussinesq equations and the energy equation. The reduced basis is constructed with a Proper Orthogonal Decomposition (POD) approach and to obtain the Reduced Order Model, a Galerkin projection of the governing equations onto the reduced basis is performed. The ROM is tested on a 2D differentially heated cavity of which the side wall temperatures are parametrized. The parametrization is done using a control function method. The aim of the method is to obtain homogeneous POD basis functions. The control functions are obtained solving a Laplacian function for temperature. Only one full order solution was required for the reduced basis creation. The obtained ROM is stable for different parameter sets for which the temperature difference between the walls is smaller than for the set in the FOM used for the POD basis creation. Then, the relative error between the FOM and the ROM for temperature is below 10−4 and for velocity below 10−1 for the vast part of the simulation time. Finally, the ROM is about 20 times faster than the FOM run on a single processor.
Building theory and applications : proceedings of M&C 2019
2452
2461
https://biblio.ugent.be/publication/8627766
http://hdl.handle.net/1854/LU-8627766
American Nuclear Society
Star, K.; Stabile, G.; Georgaka, S.; Belloni, F.; Rozza, G.; Degroote, J.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/115071
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