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42nd AIAA Aerospace Sciences Meeting and Exhibit

DOI: 10.2514/6.2004-436

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Development of a higher-order solver for aerodynamic applications

Journal article published in 2 by David L. Darmofal, Krzysztof J. Fidkowski
This paper was not found in any repository, but could be made available legally by the author.
This paper was not found in any repository, but could be made available legally by the author.

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Abstract

We present the results from the development of a higher-order discontinuous Galerkin finite element solver using p-multigrid with line Jacobi smoothing. The line smoothing al-gorithm 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 perfor-mance of line implicit versus point implicit relaxation. Through a mesh refinement study, we determine that the accuracy of the discretization is the optimal O(h p+1) for three dif-ferent smooth problems. The multigrid convergence rate is found to be independent of the polynomial order but does depend weakly on the grid size. Timing studies for each prob-lem indicate that higher order is advantageous over grid refinement when high accuracy is required.