Show simple item record

dc.contributor.authorDerlaga, Joseph Michaelen_US
dc.date.accessioned2015-07-24T08:00:11Z
dc.date.available2015-07-24T08:00:11Z
dc.date.issued2015-07-23en_US
dc.identifier.othervt_gsexam:6094en_US
dc.identifier.urihttp://hdl.handle.net/10919/54592
dc.description.abstractNumerical solutions obtained through the use of Computational Fluid Dynamics (CFD) are subject to discretization error, which is locally generated by truncation error. The discretization error is extremely difficult to properly estimate and this in turn leads to uncertainty over the quality of the numerical solutions obtained via CFD methods and the engineering functionals computed using these solutions. Adjoint error estimation techniques specifically seek to estimate the error in functionals, but are dependent upon accurate truncation error estimates. This work examines the application of new, single-grid, truncation error estimation procedures to the problem of adjoint error estimation for both the quasi-1D and 2D Euler equations. The new truncation error estimation techniques are based on local reconstructions of the computed solutions and comparisons are made for the quasi-1D study in order to determine the most appropriate solution variables to reconstruct as well as the most appropriate reconstruction method. In addition, comparisons are made between the single-grid truncation error estimates and methods based on uniformally refining or coarsening the underlying numerical mesh on which the computed solutions are obtained. A method based on an refined grid error estimate is shown to work well for a non-isentropic flow for the quasi-1D Euler equations, but all truncation error estimations methods ultimately result in over prediction of functional discretization error in the presence of a shock in 2D. Alternatives to adjoint methods, which can only estimate the error in a single functional for each adjoint solution obtained, are examined for the 2D Euler equations. The defection correction method and error transport equations are capable of locally improving the entire computed solution, allowing for error estimates in multiple functionals. It is found that all three functional discretization error estimates perform similarly for the same truncation error estimate, although the defect correction method is the most costly from a computational viewpoint. Comparisons are made between truncation error and adjoint weighted truncation error based adaptive indicators. For the quasi-1D Euler equations it is found that both methods are competitive, however the truncation error based method is cheaper as a separate adjoint solve is avoided. For the 2D Euler equations, the truncation error estimates on the adapted meshes suffer due to a lack of smooth grid transformations which are used in reconstructing the computed solutions. In order to complete this work, a new CFD code incorporating a variety of best practices from the field of Computer Science is developed as well as a new method of performing code verification using the method of manufactured solutions which is significantly easier to implement than traditional manufactured solution techniques.en_US
dc.format.mediumETDen_US
dc.publisherVirginia Techen_US
dc.rightsThis Item is protected by copyright and/or related rights. Some uses of this Item may be deemed fair and permitted by law even without permission from the rights holder(s), or the rights holder(s) may have licensed the work for use under certain conditions. For other uses you need to obtain permission from the rights holder(s).en_US
dc.subjectCFDen_US
dc.subjectadjoint methodsen_US
dc.subjectdefect correctionen_US
dc.subjecterror transport equationsen_US
dc.subjecterror estimationen_US
dc.titleApplication of Improved Truncation Error Estimation Techniques to Adjoint Based Error Estimation and Grid Adaptationen_US
dc.typeDissertationen_US
dc.contributor.departmentAerospace and Ocean Engineeringen_US
dc.description.degreePHDen_US
thesis.degree.namePHDen_US
thesis.degree.leveldoctoralen_US
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen_US
thesis.degree.disciplineAerospace Engineeringen_US
dc.contributor.committeechairRoy, Christopher Johnen_US
dc.contributor.committeememberCanfield, Robert Arthuren_US
dc.contributor.committeememberNeu, Wayne Len_US
dc.contributor.committeememberBorggaard, Jeffrey Ten_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record