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A Reconstruction Approach to High-Order Schemes Including Discontinuous Galerkin for DiffusionWe introduce a new approach to high-order accuracy for the numerical solution of diffusion problems by solving the equations in differential form using a reconstruction technique. The approach has the advantages of simplicity and economy. It results in several new high-order methods including a simplified version of discontinuous Galerkin (DG). It also leads to new definitions of common value and common gradient quantities at each interface shared by the two adjacent cells. In addition, the new approach clarifies the relations among the various choices of new and existing common quantities. Fourier stability and accuracy analyses are carried out for the resulting schemes. Extensions to the case of quadrilateral meshes are obtained via tensor products. For the two-point boundary value problem (steady state), it is shown that these schemes, which include most popular DG methods, yield exact common interface quantities as well as exact cell average solutions for nearly all cases.
Document ID
20120012839
Acquisition Source
Glenn Research Center
Document Type
Conference Paper
Authors
Huynh, H. T. (NASA Glenn Research Center Cleveland, OH, United States)
Date Acquired
August 26, 2013
Publication Date
January 5, 2009
Subject Category
Numerical Analysis
Report/Patent Number
AIAA Paper 2009-403
E-18251
Meeting Information
Meeting: 47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition
Location: Orlando, FL
Country: United States
Start Date: January 5, 2009
End Date: January 8, 2009
Sponsors: American Inst. of Aeronautics and Astronautics
Funding Number(s)
WBS: WBS 599489.02.07.03.03.03.03
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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