Proper quantification and propagation of uncertainties in computational simulations are of critical importance. This issue is especially challenging for computational fluid dynamics (CFD) applications. A particular obstacle for uncertainty quantifications in CFD problems is the large model discrepancies associated with the CFD models used for uncertainty propagation. Neglecting or improperly representing the model discrepancies leads to inaccurate and distorted uncertainty distribution for the quantities of interest (QoI). High-fidelity models, being accurate yet expensive, can accommodate only a small ensemble of simulations and thus lead to large interpolation errors and/or sampling errors; low-fidelity models can propagate a large ensemble, but can introduce large modeling errors. In this work, we propose a multimodel strategy to account for the influences of model discrepancies in uncertainty propagation and to reduce their impact on the predictions. Specifically, we take advantage of CFD models of multiple fidelities to estimate the model discrepancies associated with the lower-fidelity model in the parameter space. A Gaussian process (GP) is adopted to construct the model discrepancy function, and a Bayesian approach is used to infer the discrepancies and corresponding uncertainties in the regions of the parameter space where the high-fidelity simulations are not performed. Several examples of relevance to CFD applications are performed to demonstrate the merits of the proposed strategy. Simulation results suggest that, by combining low- and high-fidelity models, the proposed approach produces better results than what either model can achieve individually.
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March 2018
Research-Article
Propagation of Input Uncertainty in Presence of Model-Form Uncertainty: A Multifidelity Approach for Computational Fluid Dynamics Applications
Jian-Xun Wang,
Jian-Xun Wang
Department of Aerospace and
Ocean Engineering,
Virginia Tech,
Blacksburg, VA 24060
Ocean Engineering,
Virginia Tech,
Blacksburg, VA 24060
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Christopher J. Roy,
Christopher J. Roy
Department of Aerospace and
Ocean Engineering,
Virginia Tech,
Blacksburg, VA 24060
Ocean Engineering,
Virginia Tech,
Blacksburg, VA 24060
Search for other works by this author on:
Heng Xiao
Heng Xiao
Department of Aerospace and
Ocean Engineering,
Virginia Tech,
Blacksburg, VA 24060
e-mail: hengxiao@vt.edu (Heng Xiao)
Ocean Engineering,
Virginia Tech,
Blacksburg, VA 24060
e-mail: hengxiao@vt.edu (Heng Xiao)
Search for other works by this author on:
Jian-Xun Wang
Department of Aerospace and
Ocean Engineering,
Virginia Tech,
Blacksburg, VA 24060
Ocean Engineering,
Virginia Tech,
Blacksburg, VA 24060
Christopher J. Roy
Department of Aerospace and
Ocean Engineering,
Virginia Tech,
Blacksburg, VA 24060
Ocean Engineering,
Virginia Tech,
Blacksburg, VA 24060
Heng Xiao
Department of Aerospace and
Ocean Engineering,
Virginia Tech,
Blacksburg, VA 24060
e-mail: hengxiao@vt.edu (Heng Xiao)
Ocean Engineering,
Virginia Tech,
Blacksburg, VA 24060
e-mail: hengxiao@vt.edu (Heng Xiao)
1Corresponding author.
Manuscript received August 10, 2016; final manuscript received December 27, 2016; published online September 7, 2017. Assoc. Editor: Yan Wang.
ASME J. Risk Uncertainty Part B. Mar 2018, 4(1): 011002 (8 pages)
Published Online: September 7, 2017
Article history
Received:
August 10, 2016
Revised:
December 27, 2016
Citation
Wang, J., Roy, C. J., and Xiao, H. (September 7, 2017). "Propagation of Input Uncertainty in Presence of Model-Form Uncertainty: A Multifidelity Approach for Computational Fluid Dynamics Applications." ASME. ASME J. Risk Uncertainty Part B. March 2018; 4(1): 011002. https://doi.org/10.1115/1.4037452
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