Reduced-order models for parameter dependent geometries based on shape sensitivity analysis

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DOIResolve DOI: http://doi.org/10.1016/j.jcp.2009.10.033
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TypeArticle
Journal titleJournal of Computational Physics
Volume229
Issue4
Pages13271352; # of pages: 26
SubjectProper orthogonal decomposition; Reduced-order models; Sensitivity analysis; Shape parameters; Burgers’ equation; Navier–Stokes equations
AbstractThe proper orthogonal decomposition (POD) is widely used to derive low-dimensional models of large and complex systems. One of the main drawback of this method, however, is that it is based on reference data. When they are obtained for one single set of parameter values, the resulting model can reproduce the reference dynamics very accurately but generally lack of robustness away from the reference state. It is therefore crucial to enlarge the validity range of these models beyond the parameter values for which they were derived. This paper presents two strategies based on shape sensitivity analysis to partially address this limitation of the POD for parameters that define the geometry of the problem at hand (design or shape parameters.) We first detail the methodology to compute both the POD modes and their Lagrangian sensitivities with respect to shape parameters. From them, we derive improved reduced-order bases to approximate a class of solutions over a range of parameter values. Secondly, we demonstrate the efficiency and limitations of these approaches on two typical flow problems: (1) the one-dimensional Burgers’ equation; (2) the two-dimensional flows past a square cylinder over a range of incidence angles.
Publication date
LanguageEnglish
AffiliationNational Research Council Canada (NRC-CNRC); NRC Industrial Materials Institute
Peer reviewedYes
NRC number52491
NPARC number15236575
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Record identifierb6180adf-7a3a-4e34-b650-cf81a1df0001
Record created2010-05-13
Record modified2016-05-09
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