Advances in computational fluid dynamics with discrete entropy properties : stability, unstructured grids, and adaptivity
Authors
Crean, Jared
ORCID
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Other Contributors
Hicken, Jason
Shephard, M. S. (Mark S.)
Sahni, Onkar
Banks, Jeffrey
Shephard, M. S. (Mark S.)
Sahni, Onkar
Banks, Jeffrey
Issue Date
2019-12
Keywords
Aeronautical engineering
Degree
PhD
Terms of Use
This electronic version is a licensed copy owned by Rensselaer Polytechnic Institute, Troy, NY. Copyright of original work retained by author.
Full Citation
Abstract
The second part of this thesis is a method to rapidly compute approximate functional values for mildly nonlinear problems. This method extends the theory of the adjoint to incorporate changes to both the solution and the geometry simultaneously. By using the solution on an initial geometry, the solution on the new geometry can be computed by solving the governing equations on a subset of the domain. The accurate prediction of which portions of the domain should be re-solved depends on the nonlinearity of the problem, and the proposed reanalysis method is accurate for problems where the strength of the nonlinearity is limited. The final part of this thesis is an $r$-adaptation method that uses the properties of the entropy-stable discretization to change the mesh node coordinates. This method uses an optimization problem to minimize the dissipation introduced by the discretization, which can be interpreted as reducing the magnitude of the modes that cannot be represented on the given mesh. The effect is that the mesh is aligned with flow features, leading to improvements in both solution and drag coefficient error for the example aerodynamic problems considered.
Description
December 2019
School of Engineering
School of Engineering
Department
Dept. of Mechanical, Aerospace, and Nuclear Engineering
Publisher
Rensselaer Polytechnic Institute, Troy, NY
Relationships
Rensselaer Theses and Dissertations Online Collection
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