2026-09-19T14:40:42Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/288862022-01-13T07:54:11Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
David L. Darmofal.
Oliver, Todd A., 1980-
Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics.
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
2005-09-27T18:52:45Z
2005-09-27T18:52:45Z
2004
2004
http://hdl.handle.net/1721.1/28886
60426576
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2004.
Includes bibliographical references (p. 69-74).
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(Ìp+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.
by Todd A. Oliver.
S.M.
74 p.
3542125 bytes
3548300 bytes
application/pdf
application/pdf
en_US
Massachusetts Institute of Technology
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
Aeronautics and Astronautics.
Multigrid solution for high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations
Thesis
application/pdf
false
Publication
unknown
unknown
<Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="7be77f8d-83e2-4bec-aee4-d4b2314acb37">
<Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type>
<Language>en_US</Language>
<Title>Multigrid solution for high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations</Title>
<PublishedIn>
<Publication>
</Publication>
</PublishedIn>
<PublicationDate>2004</PublicationDate>
<Authors>
<Author>
<DisplayName>Oliver, Todd A., 1980-</DisplayName>
<Affiliation>
<OrgUnit>
</OrgUnit>
</Affiliation>
</Author>
</Authors>
<Editors>
</Editors>
<Publishers>
<Publisher>
<DisplayName>Massachusetts Institute of Technology</DisplayName>
<OrgUnit />
</Publisher>
</Publishers>
<License>http://dspace.mit.edu/handle/1721.1/7582</License>
<Keyword>Aeronautics and Astronautics.</Keyword>
<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(Ì‚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.</Abstract>
<Access xmlns="http://purl.org/coar/access_right"
>
</Access>
</Publication>