A new Richardson extrapolation-based uncertainty estimator is developed which utilizes a global order of accuracy. The most significant difference between the proposed uncertainty estimator (referred to as the global deviation uncertainty estimator) and others in the literature is that we compute uncertainty estimates at all cells/nodes in the domain regardless of the local convergence behavior (i.e., even if the local solution is oscillatory with grid refinement). Various metrics are used to quantitatively calibrate and evaluate the uncertainty estimator compared to the true solution. The metrics are used to assess the global deviation uncertainty estimator compared to other commonly used uncertainty estimators of the same type such as the original grid convergence index (GCI) and the factor of safety method. Four two-dimensional, steady, inviscid flow fields with exact solutions are used to calibrate the parameters in the proposed uncertainty estimator and make up about 30% of the total solution data set. The evaluation data set is composed of several additional steady, two-dimensional and three-dimensional solutions computed using different computational fluid dynamics codes with exact solutions including a zero pressure gradient turbulent flat plate with a well-defined numerical benchmark. All solutions are formally first- or second-order accurate. The global deviation uncertainty estimator is developed using an empirical approach with a focus on local variables and shows significant improvement compared to existing extrapolation-based uncertainty estimates, even when applied to regions where the local convergence behavior is divergent or oscillatory.
Skip Nav Destination
Article navigation
December 2016
Research-Article
A New Extrapolation-Based Uncertainty Estimator for Computational Fluid Dynamics
Tyrone S. Phillips,
Tyrone S. Phillips
Department of Aerospace
and Ocean Engineering,
Virginia Tech,
Blacksburg, VA 24061
e-mail: tphilli6@gmail.com
and Ocean Engineering,
Virginia Tech,
Blacksburg, VA 24061
e-mail: tphilli6@gmail.com
Search for other works by this author on:
Christopher J. Roy
Christopher J. Roy
Professor
Department of Aerospace
and Ocean Engineering,
Virginia Tech,
Blacksburg, VA 24061
e-mail: cjroy@vt.edu
Department of Aerospace
and Ocean Engineering,
Virginia Tech,
Blacksburg, VA 24061
e-mail: cjroy@vt.edu
Search for other works by this author on:
Tyrone S. Phillips
Department of Aerospace
and Ocean Engineering,
Virginia Tech,
Blacksburg, VA 24061
e-mail: tphilli6@gmail.com
and Ocean Engineering,
Virginia Tech,
Blacksburg, VA 24061
e-mail: tphilli6@gmail.com
Christopher J. Roy
Professor
Department of Aerospace
and Ocean Engineering,
Virginia Tech,
Blacksburg, VA 24061
e-mail: cjroy@vt.edu
Department of Aerospace
and Ocean Engineering,
Virginia Tech,
Blacksburg, VA 24061
e-mail: cjroy@vt.edu
Manuscript received December 2, 2014; final manuscript received December 22, 2016; published online January 20, 2017. Editor: Ashley F. Emery.
J. Verif. Valid. Uncert. Dec 2016, 1(4): 041006 (13 pages)
Published Online: January 20, 2017
Article history
Received:
December 2, 2014
Revised:
December 22, 2016
Citation
Phillips, T. S., and Roy, C. J. (January 20, 2017). "A New Extrapolation-Based Uncertainty Estimator for Computational Fluid Dynamics." ASME. J. Verif. Valid. Uncert. December 2016; 1(4): 041006. https://doi.org/10.1115/1.4035666
Download citation file:
Get Email Alerts
Cited By
Influence of Sampling Rate on Reproducibility and Accuracy of Miniature Kolsky Bar Experiments
J. Verif. Valid. Uncert
Reviewer's Recognition
J. Verif. Valid. Uncert (March 2024)
Approximate Integral Method for Nonlinear Reliability Analysis
J. Verif. Valid. Uncert
Related Articles
Richardson Extrapolation-Based Discretization Uncertainty Estimation for Computational Fluid Dynamics
J. Fluids Eng (December,2014)
Discussion: Criticisms of the “Correction Factor” Verification Method
J. Fluids Eng (July,2004)
Related Proceedings Papers
Related Chapters
Sandia Heat Flux Gauge Thermal Response and Uncertainty Models
Thermal Measurements: The Foundation of Fire Standards
Minimum Factor of Safety and Failure Mechanism in Slope Stability Analysis
Geological Engineering: Proceedings of the 1 st International Conference (ICGE 2007)
Understanding The Systematic Error of a Mineral-Insulated, Metal Sheathed (MIMS) Thermocouple Attached to a Heated Flat Surface
Thermal Measurements: The Foundation of Fire Standards