Stabilized weighted reduced basis methods for parametrized advection dominated problems with random inputs

Davide Torlo, Francesco Ballarin, Gianluigi Rozza

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

In this work, we propose viable and eficient strategies for stabilized parametrized advection dominated problems, with random inputs. In particular, we investigate the combination of the wRB (weighted reduced basis) method for stochastic parametrized problems with the stabilized RB (reduced basis) method, which is the integration of classical stabilization methods (streamline/upwind Petrov-Galerkin (SUPG) in our case) in the ofine-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-fdelity solutions. We present numerical test cases to assess the performance of the proposed methods in steady and unsteady problems related to heat transfer phenomena.
Original languageEnglish
Pages (from-to)1475-1502
Number of pages28
JournalSIAM/ASA JOURNAL ON UNCERTAINTY QUANTIFICATION
Volume6
DOIs
Publication statusPublished - 2018

Keywords

  • Advection dominated problems
  • Random inputs
  • Reduced basis methods
  • Stochastic parametrized advection-difusion equations
  • Uncertainty quantifcation

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