Vol. 7, No. 2, 2012

Download this article
Download this article For screen
For printing
Recent Issues
Volume 12, Issue 1
Volume 11, Issue 2
Volume 11, Issue 1
Volume 10, Issue 2
Volume 10, Issue 1
Volume 9, Issue 2
Volume 9, Issue 1
Volume 8, Issue 1
Volume 7, Issue 2
Volume 7, Issue 1
Volume 6, Issue 1
Volume 5, Issue 2
Volume 5, Issue 1
Volume 4, Issue 1
Volume 3, Issue 1
Volume 2, Issue 1
Volume 1, Issue 1
The Journal
Subscriptions
Editorial Board
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 2157-5452 (e-only)
ISSN: 1559-3940 (print)
Discontinuous Galerkin method with the spectral deferred correction time-integration scheme and a modified moment limiter for adaptive grids

Leandro D. Gryngarten, Andrew Smith and Suresh Menon

Vol. 7 (2012), No. 2, 133–174
Abstract

The discontinuous Galerkin (DG) method is combined with the spectral deferred correction (SDC) time integration approach to solve the fluid dynamic equations. The moment limiter is generalized for nonuniform grids with hanging nodes that result from adaptive mesh refinement. The effect of characteristic, primitive, or conservative decomposition in the limiting stage is studied. In general, primitive variable decomposition is a better option, especially in two and three dimensions. The accuracy-preserving total variation diminishing (AP-TVD) marker for troubled-cell detection, which uses an averaged-derivative basis, is modified to use the Legendre polynomial basis. Given that the latest basis is generally used for DG, the new approach avoids transforming to the averaged-derivative basis, what results in a more efficient technique. Further, a new error estimator is proposed to determine where to refine or coarsen the grid. This estimator is compared against other estimator used in the literature and shows an improved performance. Canonical tests in one, two, and three dimensions are conducted to show the accuracy of the solver.

Keywords
discontinuous Galerkin, moment limiter, high-order accuracy, adaptive mesh, troubled-cell detector, spectral deferred correction
Mathematical Subject Classification 2010
Primary: 35L65, 35L67, 65L06, 65M50, 65M60
Milestones
Received: 15 December 2010
Revised: 8 April 2012
Accepted: 16 April 2012
Published: 16 October 2012
Authors
Leandro D. Gryngarten
Aerospace Engineering
Georgia Institute of Techonology
270 Ferst Drive
Atlanta, GA 30332
United States
Andrew Smith
Aerospace Engineering
Georgia Institute of Techonology
270 Ferst Drive
Atlanta, GA 30332
United States
Suresh Menon
Aerospace Engineering
Georgia Institute of Techonology
270 Ferst Drive
Atlanta, GA 30332
United States