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Reduced Basis Approximation and Error Bounds for Potential Flows in Parametrized Geometries

Reduced Basis Approximation and Error Bounds for Potential Flows in Parametrized Geometries
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Year:    2011

Communications in Computational Physics, Vol. 9 (2011), Iss. 1 : pp. 1–48

Abstract

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 linear-functional 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.100310.260710a

Communications in Computational Physics, Vol. 9 (2011), Iss. 1 : pp. 1–48

Published online:    2011-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    48

Keywords:   

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