A sparse grid method for Bayesian uncertainty quantification with application to large eddy simulation turbulence models

Hoang Tran, Clayton G. Webster, Guannan Zhang

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

4 Scopus citations

Abstract

There is wide agreement that the accuracy of turbulence models suffer from their sensitivity with respect to physical input data, the uncertainties of user-elected parameters, as well as the model inadequacy. However, the application of Bayesian inference to systematically quantify the uncertainties in parameters, by means of exploring posterior probability density functions (PPDFs), has been hindered by the prohibitively daunting computational cost associated with the large number of model executions, in addition to daunting computation time per one turbulence simulation. In this effort, we perform in this paper an adaptive hierarchical sparse grid surrogate modeling approach to Bayesian inference of large eddy simulation (LES). First, an adaptive hierarchical sparse grid surrogate for the output of forward models is constructed using a relatively small number of model executions. Using such surrogate, the likelihood function can be rapidly evaluated at any point in the parameter space without simulating the computationally expensive LES model. This method is essentially similar to those developed in Zhang et al. (Water Resour Res 49:6871-6892, 2013) for geophysical and groundwater models, but is adjusted and applied here for a much more challenging problem of uncertainty quantification of turbulence models. Through a numerical demonstration of the Smagorinsky model of two-dimensional flow around a cylinder at sub-critical Reynolds number, our approach is proven to significantly reduce the number of costly LES executions without losing much accuracy in the posterior probability estimation. Here, the model parameters are calibrated against synthetic data related to the mean flow velocity and Reynolds stresses at different locations in the flow wake. The influence of the user-elected LES parameters on the quality of output data will be discussed.

Original languageEnglish
Title of host publicationSparse Grids and Applications, 2014
EditorsDirk Pflüger, Jochen Garcke
PublisherSpringer Verlag
Pages291-313
Number of pages23
ISBN (Print)9783319282602
DOIs
StatePublished - 2016
Event3rd Workshop on Sparse Grids and Applications, SGA 2014 - Stuttgart, Germany
Duration: Sep 1 2014Sep 5 2014

Publication series

NameLecture Notes in Computational Science and Engineering
Volume109
ISSN (Print)1439-7358

Conference

Conference3rd Workshop on Sparse Grids and Applications, SGA 2014
Country/TerritoryGermany
CityStuttgart
Period09/1/1409/5/14

Funding

This material is based upon work supported in part by the U.S. Air Force of Scientific Research under grant numbers 1854-V521-12; by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under contract numbers ERKJ259, ERKJE45; and by the Laboratory Directed Research and Development program at the Oak Ridge National Laboratory, which is operated by UT-Battelle, LLC., for the U.S. Department of Energy under Contract DE-AC05-00OR22725.

FundersFunder number
U.S. Air Force of Scientific Research1854-V521-12
U.S. Department of Energy
Office of Science
Advanced Scientific Computing ResearchERKJ259, ERKJE45
Laboratory Directed Research and DevelopmentDE-AC05-00OR22725

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