A high-order discontinuous Galerkin multigrid solver for aerodynamic applications
Author(s)Fidkowski, Krzysztof J., 1981-
Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics.
David L. Darmofal.
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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.
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2004.Includes bibliographical references (p. 87-90).This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
DepartmentMassachusetts Institute of Technology. Dept. of Aeronautics and Astronautics.
Massachusetts Institute of Technology
Aeronautics and Astronautics.