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Multigrid solution for high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations

Author(s)
Oliver, Todd A., 1980-
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Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics.
Advisor
David L. Darmofal.
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M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582
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Abstract
A high-order discontinuous Galerkin finite element discretization and p-multigrid solution procedure for the compressible Navier-Stokes equations are presented. The discretization has an element-compact stencil such that only elements sharing a face are coupled, regardless of the solution space. This limited coupling maximizes the effectiveness of the p-multigrid solver, which relies on an element-line Jacobi smoother. The element-line Jacobi smoother solves implicitly on lines of elements formed based on the coupling between elements in a p = 0 discretization of the scalar transport equation. Fourier analysis of 2-D scalar convection-diffusion shows that the element-line Jacobi smoother as well as the simpler element Jacobi smoother are stable independent of p and flow condition. Mesh refinement studies for simple problems with analytic solutions demonstrate that the discretization achieves optimal order of accuracy of O(h(̂p+l)). A subsonic, airfoil test case shows that the multigrid convergence rate is independent of p but weakly dependent on h. Finally, higher-order is shown to outperform grid refinement in terms of the time required to reach a desired accuracy level.
Description
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2004.
 
Includes bibliographical references (p. 69-74).
 
Date issued
2004
URI
http://hdl.handle.net/1721.1/28886
Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Publisher
Massachusetts Institute of Technology
Keywords
Aeronautics and Astronautics.

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