Four-dimensional anisotropic mesh adaptation for spacetime numerical simulations
Name
1119666580-MIT.pdf
Size
4.29 MB
Format
Adobe PDF
Checksum (MD5)
bb6b3a1891352b4263d5ec34c5fc0e31
Author(s)
Caplan, Philip Claude Delhaye.
Advisor(s)
David L. Darmofal, Robert Haimes and Jaume Peraire.
Date Issued
2019
Publisher
Massachusetts Institute of Technology
Abstract
Engineers and scientists are increasingly relying on high-fidelity numerical simulations. Within these simulations, mesh adaptation is useful for obtaining accurate predictions of an output of interest subject to a computational cost constraint. In the quest for accurately predicting outputs in problems with time-dependent solution features, a fully unstructured coupled spacetime approach has been shown to be useful in reducing the cost of the overall simulation. However, for the simulation of unsteady three-dimensional partial differential equations (PDEs), a four-dimensional mesh adaptation tool is needed. This work develops the first anisotropic metric-conforming four-dimensional mesh adaptation tool for performing adaptive numerical simulations of unsteady PDEs in three dimensions. The theory and implementation details behind our algorithm are first developed alongside an algorithm for constructing four-dimensional geometry representations.
We then demonstrate our algorithm on three-dimensional benchmark cases and it appears to outperform existing implementations, both in metric-conformity and expected tetrahedra counts. We study the utility of the mesh adaptation components to justify the design of our algorithm. We then develop four-dimensional benchmark cases and demonstrate that metric-conformity and expected pentatope counts are also achieved. This is the first time anisotropic four-dimensional meshes have been presented in the literature. Next, the entire mesh adaptation framework, Mesh Optimization via Error Sampling and Synthesis (MOESS), is extended to the context of finding the optimal mesh to represent a function of four variables. The mesh size and aspect ratio distributions of the optimized meshes match the analytic ones, thus verifying our framework.
Finally, we apply MOESS in conjunction with the mesh adaptation tool to perform the first four-dimensional anisotropic mesh adaptation for the solution of the advection-diffusion equation. The optimized meshes effectively refine the solution features corresponding to both a boundary layer solution as well as an expanding spherical wave.
Description
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2019
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages [135]-142).
Subjects
Aeronautics and Astronautics.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Terms of Use
MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission.
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