In this work, we propose viable and efficient strategies for stabilized parametrized advection dominated problems, with random inputs. In particular, we investigate the combination of wRB (weighted reduced basis) method for stochastic parametrized problems with stabilized reduced basis method, which is the integration of classical stabilization methods (SUPG, in our case) in the Offline--Online structure of the RB method. Moreover, we introduce a reduction method that selectively enables online stabilization; this leads to a sensible reduction of computational costs, while keeping a very good accuracy with respect to high fidelity solutions. We present numerical test cases to assess the performance of the proposed methods in steady and unsteady problems related to heat transfer phenomena.

Stabilized Weighted Reduced Basis Methods for Parametrized Advection Dominated Problems with Random Inputs / Torlo, Davide; Ballarin, Francesco; Rozza, Gianluigi. - In: SIAM/ASA JOURNAL ON UNCERTAINTY QUANTIFICATION. - ISSN 2166-2525. - 6:4(2018), pp. 1475-1502. [10.1137/17M1163517]

Stabilized Weighted Reduced Basis Methods for Parametrized Advection Dominated Problems with Random Inputs

Torlo, Davide;Ballarin, Francesco;Rozza, Gianluigi
2018-01-01

Abstract

In this work, we propose viable and efficient strategies for stabilized parametrized advection dominated problems, with random inputs. In particular, we investigate the combination of wRB (weighted reduced basis) method for stochastic parametrized problems with stabilized reduced basis method, which is the integration of classical stabilization methods (SUPG, in our case) in the Offline--Online structure of the RB method. Moreover, we introduce a reduction method that selectively enables online stabilization; this leads to a sensible reduction of computational costs, while keeping a very good accuracy with respect to high fidelity solutions. We present numerical test cases to assess the performance of the proposed methods in steady and unsteady problems related to heat transfer phenomena.
2018
6
4
1475
1502
https://epubs.siam.org/doi/abs/10.1137/17M1163517
https://arxiv.org/abs/1711.11275v2
https://mathlab.sissa.it/cse-software
Torlo, Davide; Ballarin, Francesco; Rozza, Gianluigi
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/85374
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