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

Ballarin, Francesco;Rozza, Gianluigi
2018

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.
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
File in questo prodotto:
File Dimensione Formato  
M116351-1.pdf

accesso aperto

Tipologia: Documento in Post-print
Licenza: Non specificato
Dimensione 1.25 MB
Formato Adobe PDF
1.25 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/85374
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 10
  • ???jsp.display-item.citation.isi??? 10
social impact