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dc.contributor.authorPhillips, Tyroneen_US
dc.date.accessioned2014-03-14T20:32:45Z
dc.date.available2014-03-14T20:32:45Z
dc.date.issued2012-02-27en_US
dc.identifier.otheretd-03192012-173723en_US
dc.identifier.urihttp://hdl.handle.net/10919/31504
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_US
dc.publisherVirginia Techen_US
dc.relation.haspartPhillips_TS_T_2012.pdfen_US
dc.rightsI hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to Virginia Tech or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report.en_US
dc.subjectRichardson Extrapolationen_US
dc.subjectNavier-Stokesen_US
dc.subjectGrid Convergence Indexen_US
dc.subjectFinite Volume Methoden_US
dc.subjectEuleren_US
dc.titleExtrapolation-based Discretization Error and Uncertainty Estimation in Computational Fluid Dynamicsen_US
dc.typeThesisen_US
dc.contributor.departmentAerospace and Ocean Engineeringen_US
dc.description.degreeMaster of Scienceen_US
thesis.degree.nameMaster of Scienceen_US
thesis.degree.levelmastersen_US
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen_US
thesis.degree.disciplineAerospace and Ocean Engineeringen_US
dc.contributor.committeechairRoy, Christopher Johnen_US
dc.contributor.committeememberCliff, Eugene M.en_US
dc.contributor.committeememberMason, William H.en_US
dc.contributor.committeememberTafti, Danesh K.en_US
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-03192012-173723/en_US
dc.date.sdate2012-03-19en_US
dc.date.rdate2012-04-26
dc.date.adate2012-04-26en_US


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