Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2014, Article ID 176752, 20 pages
http://dx.doi.org/10.1155/2014/176752
Research Article

A Third Order Accurate Cellwise Relaxation Implicit Discontinuous Galerkin Scheme for Unstructured Hybrid Meshes

1Department of Aerospace Engineering, Tohoku University, 6-6-01 Aramaki-Aza-Aoba, Aoba-ku, Sendai 980-8579, Japan
2Institute of Aeronautical Technology, Japan Aerospace Exploration Agency, 7-44-1 Jindaiji-Higashi, Chofu, Tokyo 182-8522, Japan

Received 29 December 2013; Accepted 27 May 2014; Published 8 July 2014

Academic Editor: Yonghong Wu

Copyright © 2014 Hiroyuki Asada et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. B. Cockburn and C.-W. Shu, “TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. II. GENeral framework,” Mathematics of Computation, vol. 52, no. 186, pp. 411–435, 1989. View at Publisher · View at Google Scholar · View at MathSciNet
  2. H. Luo, J. D. Baum, and R. Lohner, “A p-multigrid discontinuous Galerkin method for the Euler equations on unstructured grids,” Journal of Computational Physics, vol. 211, no. 2, pp. 767–783, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. K. Yasue, M. Furudate, N. Ohnishi, and K. Sawada, “Implicit discontinuous Galerkin method for RANS simulation utilizing pointwise relaxation algorithm,” Communications in Computational Physics, vol. 7, no. 3, pp. 510–533, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. K. Sawada and K. Yasue, “A linear stability analysis of the cell-wise relaxation implicit discontinuous Galerkin method for wave propagation,” Fluid Dynamics Research, vol. 43, no. 4, Article ID 041402, 18 pages, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. D. A. Dunavant, “High degree efficient symmetrical Gaussian quadrature rules for the triangle,” International Journal for Numerical Methods in Engineering, vol. 21, no. 6, pp. 1129–1148, 1985. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. Y. Liu and M. Vinokur, “Exact integrations of polynomials and symmetric quadrature formulas over arbitrary polyhedral grids,” Journal of Computational Physics, vol. 140, no. 1, pp. 122–147, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  7. T. C. Warburton, Spectral/hp methods on polymorphic multi-domains: algorithms and applications [Ph.D. thesis], Center for Fluid Mechanics, Division of Applied Mathematics, Brown University, Providence, RI, USA, 1998.
  8. F. Bassi and S. Rebay, “G{MRES} discontinuous GALerkin solution of the compressible Navier-Stokes equations,” in Discontinuous Galerkin Methods, vol. 11 of Lecture Notes in Computational Science and Engineering, pp. 197–208, Springer, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  9. D. N. Arnold, F. Brezzi, B. Cockburn, and D. Marini, “Discontinuous Galerkin methods for elliptic problems,” in Discontinuous Galerkin Methods, vol. 11 of Lecture Notes in Computational Science and Engineering, pp. 89–101, Springer, Berlin, Germany, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  10. U. Brennenstuhl and D. Hummel, “Vortex formation over double-delta wings,” ICAS 82-6.6.3, 1982. View at Google Scholar
  11. G. Karypis and V. Kumar, “A fast and high quality multilevel scheme for partitioning irregular graphs,” SIAM Journal on Scientific Computing, vol. 20, no. 1, pp. 359–392, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus