A high-order discontinuous Galerkin multigrid solver for aerodynamic applications

Results are presented from the development of a high-order discontinuous Galerkin finite element solver using p-multigrid with line Jacobi smoothing. The line smoothing algorithm is presented for unstructured meshes, and p-multigrid is outlined for the nonlinear Euler equations of gas dynamics. Analysis of 2-D advection shows the improved performance of line implicit versus block implicit relaxation. Through a mesh refinement study, the accuracy of the discretization is determined to be the optimal O(h[superscript]P+l) for smooth problems in 2-D and 3-D. The multigrid convergence rate is found to be independent of the interpolation order but weakly dependent on the grid size. Timing studies for each problem indicate that higher order is advantageous over grid refinement when high accuracy is required. Finally, parallel versions of the 2-D and 3-D solvers demonstrate close to ideal coarse-grain scalability.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2004

Author dc:creator

• Fidkowski, Krzysztof J., 1981-

Advisor dc:contributor.advisor

• David L. Darmofal.

• Aeronautics and Astronautics.

Statement dc:rights

• 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.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/16657

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/16657