Translator Disclaimer
2012 Discontinuous Galerkin method with the spectral deferred correction time-integration scheme and a modified moment limiter for adaptive grids
Leandro Gryngarten, Andrew Smith, Suresh Menon
Commun. Appl. Math. Comput. Sci. 7(2): 133-174 (2012). DOI: 10.2140/camcos.2012.7.133

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.

Citation

Download Citation

Leandro Gryngarten. Andrew Smith. Suresh Menon. "Discontinuous Galerkin method with the spectral deferred correction time-integration scheme and a modified moment limiter for adaptive grids." Commun. Appl. Math. Comput. Sci. 7 (2) 133 - 174, 2012. https://doi.org/10.2140/camcos.2012.7.133

Information

Received: 15 December 2010; Revised: 8 April 2012; Accepted: 16 April 2012; Published: 2012
First available in Project Euclid: 20 December 2017

zbMATH: 06130512
MathSciNet: MR3005736
Digital Object Identifier: 10.2140/camcos.2012.7.133

Subjects:
Primary: 35L65, 35L67, 65L06, 65M50, 65M60

Rights: Copyright © 2012 Mathematical Sciences Publishers

JOURNAL ARTICLE
42 PAGES


SHARE
Vol.7 • No. 2 • 2012
MSP
Back to Top