Extrapolation-based Discretization Error and Uncertainty Estimation in Computational Fluid Dynamics

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dc.contributor.authorPhillips, Tyroneen
dc.contributor.committeechairRoy, Christopher J.en
dc.contributor.committeememberCliff, Eugene M.en
dc.contributor.committeememberMason, William H.en
dc.contributor.committeememberTafti, Danesh K.en
dc.contributor.departmentAerospace and Ocean Engineeringen
dc.date.accessioned2014-03-14T20:32:45Zen
dc.date.adate2012-04-26en
dc.date.available2014-03-14T20:32:45Zen
dc.date.issued2012-02-27en
dc.date.rdate2012-04-26en
dc.date.sdate2012-03-19en
dc.description.abstractThe solution to partial differential equations generally requires approximations that result in numerical error in the final solution. Of the different types of numerical error in a solution, discretization error is the largest and most difficult error to estimate. In addition, the accuracy of the discretization error estimates relies on the solution (or multiple solutions used in the estimate) being in the asymptotic range. The asymptotic range is used to describe the convergence of a solution, where an asymptotic solution approaches the exact solution at a rate proportional to the change in mesh spacing to an exponent equal to the formal order of accuracy. A non-asymptotic solution can result in unpredictable convergence rates introducing uncertainty in discretization error estimates. To account for the additional uncertainty, various discretization uncertainty estimators have been developed. The goal of this work is to evaluation discretization error and discretization uncertainty estimators based on Richardson extrapolation for computational fluid dynamics problems. In order to evaluate the estimators, the exact solution should be known. A select set of solutions to the 2D Euler equations with known exact solutions are used to evaluate the estimators. Since exact solutions are only available for trivial cases, two applications are also used to evaluate the estimators which are solutions to the Navier-Stokes equations: a laminar flat plate and a turbulent flat plate using the k-Ï SST turbulence model. Since the exact solutions to the Navier-Stokes equations for these cases are unknown, numerical benchmarks are created which are solutions on significantly finer meshes than the solutions used to estimate the discretization error and uncertainty. Metrics are developed to evaluate the accuracy of the error and uncertainty estimates and to study the behavior of each estimator when the solutions are in, near, and far from the asymptotic range. Based on the results, general recommendations are made for the implementation of the error and uncertainty estimators. In addition, a new uncertainty estimator is proposed with the goal of combining the favorable attributes of the discretization error and uncertainty estimators evaluated. The new estimator is evaluated using numerical solutions which were not used for development and shows improved accuracy over the evaluated estimators.en
dc.description.degreeMaster of Scienceen
dc.identifier.otheretd-03192012-173723en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-03192012-173723/en
dc.identifier.urihttp://hdl.handle.net/10919/31504en
dc.publisherVirginia Techen
dc.relation.haspartPhillips_TS_T_2012.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectRichardson Extrapolationen
dc.subjectNavier-Stokesen
dc.subjectGrid Convergence Indexen
dc.subjectFinite Volume Methoden
dc.subjectEuleren
dc.titleExtrapolation-based Discretization Error and Uncertainty Estimation in Computational Fluid Dynamicsen
dc.typeThesisen
thesis.degree.disciplineAerospace and Ocean Engineeringen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen

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