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Sensitivity equation method for the Navier‐Stokes equations applied to uncertainty propagation
Author(s) -
Fiorini Camilla,
Després Bruno,
Puscas Maria Adela
Publication year - 2021
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4875
Subject(s) - sensitivity (control systems) , variance (accounting) , mathematics , stability (learning theory) , uncertainty quantification , variance based sensitivity analysis , finite element method , monte carlo method , navier–stokes equations , finite volume method , mathematical optimization , computer science , statistics , compressibility , one way analysis of variance , mechanics , physics , analysis of variance , accounting , machine learning , electronic engineering , engineering , business , thermodynamics
Summary This works deals with sensitivity analysis (SA) for the Navier‐Stokes equations. The aim is to provide an estimate of the variance of the velocity field when some of the parameters are uncertain and then to use the variance to compute confidence intervals for the output of the model. First, we introduce the physical model and analyze its stability. The sensitivity equations are derived, and their stability analyzed as well. We propose a finite element‐volume numerical scheme for the state and the sensitivity, which is integrated into the open‐source industrial code TrioCFD. Finally, we present some numerical results: a steady and an unsteady test case for the channel flow problem are investigated. For the steady case, we compare the results to the Monte Carlo method and show how the SA technique succeeds in providing very accurate estimates of the variance. For the unsteady case, a new filtering procedure is proposed to deal with a sensitivity that grows in time. The filtered sensitivity is then used to compute the variance of the output and to provide confidence intervals.