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An Application of the Quadrature-Free Discontinuous Galerkin MethodThe process of generating a block-structured mesh with the smoothness required for high-accuracy schemes is still a time-consuming process often measured in weeks or months. Unstructured grids about complex geometries are more easily generated, and for this reason, methods using unstructured grids have gained favor for aerodynamic analyses. The discontinuous Galerkin (DG) method is a compact finite-element projection method that provides a practical framework for the development of a high-order method using unstructured grids. Higher-order accuracy is obtained by representing the solution as a high-degree polynomial whose time evolution is governed by a local Galerkin projection. The traditional implementation of the discontinuous Galerkin uses quadrature for the evaluation of the integral projections and is prohibitively expensive. Atkins and Shu introduced the quadrature-free formulation in which the integrals are evaluated a-priori and exactly for a similarity element. The approach has been demonstrated to possess the accuracy required for acoustics even in cases where the grid is not smooth. Other issues such as boundary conditions and the treatment of non-linear fluxes have also been studied in earlier work This paper describes the application of the quadrature-free discontinuous Galerkin method to a two-dimensional shear layer problem. First, a brief description of the method is given. Next, the problem is described and the solution is presented. Finally, the resources required to perform the calculations are given.
Document ID
Document Type
Conference Paper
Lockard, David P.
(NASA Langley Research Center Hampton, VA United States)
Atkins, Harold L.
(NASA Langley Research Center Hampton, VA United States)
Date Acquired
August 20, 2013
Publication Date
August 1, 2000
Publication Information
Publication: Third Computational Aeroacoustics (CAA) Workshop on Benchmark Problems
Subject Category
Theoretical Mathematics
Distribution Limits
Work of the US Gov. Public Use Permitted.

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IDRelationTitle20010061385Analytic PrimaryThird Computational Aeroacoustics (CAA) Workshop on Benchmark Problems
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