Reduced basis approximation and error bounds for potential flows in parametrized geometries

In this paper we consider (hierarchical, Lagrange) reduced basis approximation and a posteriori error estimation for potential flows in affinely parametrized geometries. We review the essential ingredients: i) a Galerkin projection onto a low dimensional space associated with a smooth “parametric manifold” in order to get a dimension reduction; ii) an efficient and effective greedy sampling method for identification of optimal and numerically stable approximations to have a rapid convergence; iii) an a posteriori error estimation procedure: rigorous and sharp bounds for the linearfunctional outputs of interest and over the potential solution or related quantities of interest like velocity and/or pressure; iv) an Offline-Online computational decomposition strategies to achieve a minimum marginal computational cost for high performance in the real-time and many-query (e.g., design and optimization) contexts. We present three illustrative results for inviscid potential flows in parametrized geometries representing a Venturi channel, a circular bend and an added mass problem.


Published in:
Communications in Computational Physics, 9, 1, 1-48
Year:
2011
ISSN:
1815-2406
Keywords:
Note:
preprint as MATHICSE report 11.2010
Laboratories:




 Record created 2010-07-27, last modified 2018-09-13

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