Error Transport Equations for Unsteady Discontinuous Applications

Computational Fluid Dynamics (CFD) has been pivotal in scientific computing, providing critical insights into complex fluid dynamics unattainable through traditional experimental methods. Despite its widespread use, the accuracy of CFD results remains contingent upon the underlying modeling and numerical errors. A key aspect of ensuring simulation reliability is the accurate quantification of discretization error (DE), which is the difference between the simulation solution and the exact solution in the physical world. This study addresses quantifying DE through Error Transport Equations (ETE), which are an additional set of equations capable of quantifying the local DE in a solution. Historically, Richardson extrapolation has been a mainstay for DE estimation due to its simplicity and effectiveness. However, the method's feasibility diminishes with increasing computational demands, particularly in large-scale and high-dimensional problems. The integration of ETE into existing CFD frameworks is facilitated by their compatibility with existing numerical codes, minimizing the need for extensive code modification. By incorporating techniques developed for managing discontinuities, the study broadens ETE applicability to a wider range of scientific computing applications, particularly those involving complex, unsteady flows. The culmination of this research is demonstrated on unsteady discontinuous problems, such as Sod's problem.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Aerospace Engineering

Department dc:contributor.department

Aerospace and Ocean Engineering

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2024

Author dc:creator

• Ganotaki, Michael

Chair dc:contributor.committeechair

• Roy, Christopher John

Committee members dc:contributor.committeemember

• Ferguson, Jim
• Massa, Luca

• Error estimation
• CFD
• Discontinuities

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en

Dc Identifier Other

vt_gsexam:39771

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/118593