196
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

A compact subcell WENO limiting strategy using immediate neighbours for Runge-Kutta discontinuous Galerkin methods

ORCID Icon &
Pages 608-626 | Received 09 Aug 2019, Accepted 26 Apr 2020, Published online: 23 May 2020

References

  • B. Cockburn and C.-W. Shu, The Runge-Kutta local projection P1-discontinuous Galerkin method for scalar conservation laws, M2AN 25 (1991), pp. 337–361.
  • M. Dumbser, O. Zanotti, R. Loubere, and S. Diot, A posteriori subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws, J. Comput. Phys. 278 (2014), pp. 47–75.
  • A. Harten, B. Engquist, S. Osher, and S.R. Chakravarthy, Uniformly high order accurate essentially non-oscillatory schemes, III, J. Comput. Phys. 71 (1987), pp. 231–303.
  • J.S. Hesthaven and T. Warburton, Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications, Springer, New York, 2008.
  • L. Krivodonova, J. Xin, J.-F. Remacle, N. Chevaugeon, and J. Flaherty, Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws, Appl. Numer. Math. 48 (2004), pp. 323–338.
  • J. Qiu and C.-W. Shu, A comparison of troubled-cell indicators for Runge-Kutta discontinuous Galerkin methods using weighted essentially nonoscillatory limiters, SIAM J. Sci. Comput. 27 (2005), pp. 995–1013.
  • J. Qiu and C.-W. Shu, Runge-Kutta discontinuous Galerkin method using WENO limiters, SIAM J. Sci. Comput. 26 (2005), pp. 907–929.
  • C.-W. Shu, TVD time discretizations, SIAM J. Sci. Stat. Comput. 9 (1988), pp. 1073–1084.
  • C.-W. Shu, Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws, Lecture Notes in Mathematics, Springer, Springer-Verlag Berlin Heidelberg1998, pp. 325–432.
  • C.-W. Shu and S. Osher, Effective implementation of essentially non-oscillatory shock-capturing schemes, II, J. Comput. Phys. 83 (1989), pp. 32–78.
  • G. Sod, A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws, J. Comput. Phys. 27 (1978), pp. 1–31.
  • P. Woodward and P. Colella, The numerical simulation of two-dimensional fluid flow with strong shocks, J. Comput. Phys. 54 (1984), pp. 115–173.
  • X. Zhang and C.-W. Shu, On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes, J. Comput. Phys. 229 (2010), pp. 8918–8934.
  • X. Zhong and C.-W. Shu, A simple weighted essentially nonoscillatory limiter for Runge-Kutta discontinuous Galerkin methods, J. Comput. Phys. 232 (2013), pp. 397–415.
  • J. Zhu, X. Zhong, C.-W. Shu, and J. Qiu, Runge-Kutta discontinuous Galerkin method with a simple and compact hermite WENO limiter, Commun. Comput. Phys. 19 (2016), pp. 944–969.
  • H. Zhu, J. Qiu, and J. Zhu, A simple, high-order and compact WENO limiter for RKDG method, Comput. Math. Appl. 79 (2020), pp. 317–336.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.