Year: 2011
Communications in Computational Physics, Vol. 9 (2011), Iss. 4 : pp. 1071–1080
Abstract
In this short note we present a derivation of the Spectral Difference Scheme from a Discontinuous Galerkin (DG) discretization of a nonlinear conservation law. This allows interpretation of the Spectral Difference Scheme as a particular discretization under the quadrature-free nodal DG paradigm. Moreover, it enables identification of the key differences between the Spectral Difference Scheme and standard nodal DG schemes.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.090210.040610a
Communications in Computational Physics, Vol. 9 (2011), Iss. 4 : pp. 1071–1080
Published online: 2011-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
-
Comparison between a priori and a posteriori slope limiters for high-order finite volume schemes
Palafoutas, Jonathan | Velasco Romero, David A. | Teyssier, RomainJournal of Computational Physics, Vol. (2024), Iss. P.113571
https://doi.org/10.1016/j.jcp.2024.113571 [Citations: 0] -
Artificial viscosity-based shock capturing scheme for the Spectral Difference method on simplicial elements
Messaï, Nadir-Alexandre | Daviller, Guillaume | Boussuge, Jean-FrançoisJournal of Computational Physics, Vol. 504 (2024), Iss. P.112864
https://doi.org/10.1016/j.jcp.2024.112864 [Citations: 2] -
An arbitrary high-order Spectral Difference method for the induction equation
Han Veiga, Maria | Velasco-Romero, David A. | Wenger, Quentin | Teyssier, RomainJournal of Computational Physics, Vol. 438 (2021), Iss. P.110327
https://doi.org/10.1016/j.jcp.2021.110327 [Citations: 4] -
A stable high-order Spectral Difference method for hyperbolic conservation laws on triangular elements
Balan, Aravind | May, Georg | Schöberl, JoachimJournal of Computational Physics, Vol. 231 (2012), Iss. 5 P.2359
https://doi.org/10.1016/j.jcp.2011.11.041 [Citations: 34] -
An efficient sliding mesh interface method for high-order discontinuous Galerkin schemes
Dürrwächter, Jakob | Kurz, Marius | Kopper, Patrick | Kempf, Daniel | Munz, Claus-Dieter | Beck, AndreaComputers & Fluids, Vol. 217 (2021), Iss. P.104825
https://doi.org/10.1016/j.compfluid.2020.104825 [Citations: 12] -
A compressible high-order unstructured spectral difference code for stratified convection in rotating spherical shells
Wang, Junfeng | Liang, Chunlei | Miesch, Mark S.Journal of Computational Physics, Vol. 290 (2015), Iss. P.90
https://doi.org/10.1016/j.jcp.2015.02.047 [Citations: 10] -
A new high-order spectral difference method for simulating viscous flows on unstructured grids with mixed-element meshes
Li, Mao | Qiu, Zihua | Liang, Chunlei | Sprague, Michael | Xu, Min | Garris, Charles A.Computers & Fluids, Vol. 184 (2019), Iss. P.187
https://doi.org/10.1016/j.compfluid.2019.03.010 [Citations: 8] -
A selective immersed discontinuous Galerkin method for elliptic interface problems
He, Xiaoming | Lin, Tao | Lin, YanpingMathematical Methods in the Applied Sciences, Vol. 37 (2014), Iss. 7 P.983
https://doi.org/10.1002/mma.2856 [Citations: 26] -
A comparison of computational efficiencies of spectral difference method and correction procedure via reconstruction
Liang, Chunlei | Cox, Christopher | Plesniak, MichaelJournal of Computational Physics, Vol. 239 (2013), Iss. P.138
https://doi.org/10.1016/j.jcp.2013.01.001 [Citations: 38] -
A p-adaptive LCP formulation for the compressible Navier–Stokes equations
Cagnone, J.S. | Vermeire, B.C. | Nadarajah, S.Journal of Computational Physics, Vol. 233 (2013), Iss. P.324
https://doi.org/10.1016/j.jcp.2012.08.053 [Citations: 13] -
Handbook of Numerical Methods for Hyperbolic Problems - Basic and Fundamental Issues
Spectral Volume and Spectral Difference Methods
Wang, Z.J. | Liu, Y. | Lacor, C. | Azevedo, J.L.F.2016
https://doi.org/10.1016/bs.hna.2016.09.013 [Citations: 2] -
A collocated-grid spectral difference method for compressible flows
Chen, Wenqian | Ju, Yaping | Zhang, ChuhuaComputers & Fluids, Vol. 196 (2020), Iss. P.104341
https://doi.org/10.1016/j.compfluid.2019.104341 [Citations: 2] -
A simple, efficient, and high-order accurate curved sliding-mesh interface approach to spectral difference method on coupled rotating and stationary domains
Zhang, Bin | Liang, ChunleiJournal of Computational Physics, Vol. 295 (2015), Iss. P.147
https://doi.org/10.1016/j.jcp.2015.04.006 [Citations: 44] -
Hybridizable discontinuous Galerkin methods for second-order elliptic problems: overview, a new result and open problems
Cockburn, Bernardo
Japan Journal of Industrial and Applied Mathematics, Vol. 40 (2023), Iss. 3 P.1637
https://doi.org/10.1007/s13160-023-00603-9 [Citations: 3] -
A stable Spectral Difference approach for computations with triangular and hybrid grids up to the 6 order of accuracy
Veilleux, Adèle | Puigt, Guillaume | Deniau, Hugues | Daviller, GuillaumeJournal of Computational Physics, Vol. 449 (2022), Iss. P.110774
https://doi.org/10.1016/j.jcp.2021.110774 [Citations: 12] -
A corrected Raviart–Thomas Spectral Difference scheme stable for arbitrary order of accuracy on triangular and tetrahedral meshes
Messaï, Nadir-Alexandre | Daviller, GuillaumeComputer Methods in Applied Mechanics and Engineering, Vol. 432 (2024), Iss. P.117413
https://doi.org/10.1016/j.cma.2024.117413 [Citations: 0] -
CONVECTION IN OBLATE SOLAR-TYPE STARS
Wang, Junfeng | Miesch, Mark S. | Liang, ChunleiThe Astrophysical Journal, Vol. 830 (2016), Iss. 1 P.45
https://doi.org/10.3847/0004-637X/830/1/45 [Citations: 7] -
Quadrature-Free Implementation of a Discontinuous Galerkin Global Shallow-Water Model via Flux Correction Procedure
Nair, Ramachandran D.
Monthly Weather Review, Vol. 143 (2015), Iss. 4 P.1335
https://doi.org/10.1175/MWR-D-14-00174.1 [Citations: 3]