Computer simulations of complex mathematical models are a powerful tool for design, but they introduce uncertainties which can lead to poor design choices when simulation data is all that is available. Additionally, computational grid generation can dramatically increases the costs associated with initializing numerical simulations. Proper verification can help quantify the uncertainty in numerical simulations, and a new form of code verification is presented. This is based on the method of manufactured solutions for integral equations, which allows MMS to be used to verify shock-capturing codes. A procedure is presented for numerically evaluating the required integrals, and it is found to completely eliminate numerical error resulting from discontinuous integrand functions. Integral MMS is demonstrated, and it is found to yield convergence rates that differ by less than 5% from those obtained using differential MMS, and which match precisely with the theoretical rates for discontinuous solutions. This indicates that integral MMS can be used for code verification in place of differential MMS, which cannot be used with discontinuous solutions. Moving grids can be used to allow computed fluid motion to generate the computational grid automatically. The unique challenges associated with grid motion are explored, and multiple implementations are discussed. A software library for fluid-mechanical simulation in unsteady coordinates is also introduced. Preliminary verification of both the method and the library is discussed. The use of unsteady coordinates affects accuracy and grid convergence rates in complex ways. This work lays the foundation for future work on the use of moving grids in order to reduce the grid-generation burden for design-oriented computational fluid dynamics.
|Advisor:||Starkey, Ryan P.|
|Commitee:||Argrow, Brian, Biringen, Sedat, Daily, John, Jansen, Kenneth, Preston, Stephen|
|School:||University of Colorado at Boulder|
|School Location:||United States -- Colorado|
|Source:||DAI-B 76/10(E), Dissertation Abstracts International|
|Subjects:||Applied Mathematics, Aerospace engineering|
|Keywords:||Discontinuous integration, Discontinuous manufactured solutions, Manufactured solutions, Quadrature, Unified coordinate system, Verification|
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