Numerical analysis
Nonlinear artificial viscosity for spectral element methods
[Viscosité artificielle non linéaire pour la méthode des éléments spectraux]
Comptes Rendus. Mathématique, Tome 357 (2019) no. 7, pp. 646-654.

Nous présentons une approche basée sur les filtres pour calculer les viscosités artificielles pour la méthode des éléments spectraux. Cette procédure est simple et est mise en œuvre sur un grand nombre d'exemples.

We present a filter-based approach to computing artificial viscosities for spectral element methods. A number of applications for this approach are presented.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2019.07.006
Lu, Li 1 ; Nazarov, Murtazo 2 ; Fischer, Paul 1

1 Urbana, IL, USA
2 Uppsala, Sweden
@article{CRMATH_2019__357_7_646_0,
     author = {Lu, Li and Nazarov, Murtazo and Fischer, Paul},
     title = {Nonlinear artificial viscosity for spectral element methods},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {646--654},
     publisher = {Elsevier},
     volume = {357},
     number = {7},
     year = {2019},
     doi = {10.1016/j.crma.2019.07.006},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2019.07.006/}
}
TY  - JOUR
AU  - Lu, Li
AU  - Nazarov, Murtazo
AU  - Fischer, Paul
TI  - Nonlinear artificial viscosity for spectral element methods
JO  - Comptes Rendus. Mathématique
PY  - 2019
SP  - 646
EP  - 654
VL  - 357
IS  - 7
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2019.07.006/
DO  - 10.1016/j.crma.2019.07.006
LA  - en
ID  - CRMATH_2019__357_7_646_0
ER  - 
%0 Journal Article
%A Lu, Li
%A Nazarov, Murtazo
%A Fischer, Paul
%T Nonlinear artificial viscosity for spectral element methods
%J Comptes Rendus. Mathématique
%D 2019
%P 646-654
%V 357
%N 7
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2019.07.006/
%R 10.1016/j.crma.2019.07.006
%G en
%F CRMATH_2019__357_7_646_0
Lu, Li; Nazarov, Murtazo; Fischer, Paul. Nonlinear artificial viscosity for spectral element methods. Comptes Rendus. Mathématique, Tome 357 (2019) no. 7, pp. 646-654. doi : 10.1016/j.crma.2019.07.006. http://www.numdam.org/articles/10.1016/j.crma.2019.07.006/

[1] Argonne National Laboratory, IL, USA, Nek5000.

[2] Deville, M.; Fischer, P.; Mund, E. High-Order Methods for Incompressible Fluid Flow, Cambridge University Press, Cambridge, UK, 2002

[3] Fischer, P.; Mullen, J. Filter-based stabilization of spectral element methods, C. R. Acad. Sci. Paris, Ser. I, Volume 332 (2001) no. 3, pp. 265-270

[4] Guermond, J.; Pasquetti, R.; Popov, B. Entropy viscosity method for nonlinear conservation laws, J. Comput. Phys., Volume 230 (2011) no. 11, pp. 4248-4267

[5] Guo, B.; Ma, H.; Tadmor, E. Spectral vanishing viscosity method for nonlinear conservation laws, SIAM J. Numer. Anal., Volume 39 (2001) no. 4, pp. 1254-1268

[6] Maday, Y.; Kaber, S.; Tadmor, E. Legendre pseudospectral viscosity method for nonlinear conservation laws, SIAM J. Numer. Anal., Volume 30 (1993) no. 2, pp. 321-342

[7] Malm, J.; Schlatter, P.; Fischer, P.; Henningson, D. Stabilization of the spectral element method in convection dominated flows by recovery of skew-symmetry, J. Sci. Comput., Volume 57 (2013) no. 2, pp. 254-277

[8] Marras, S.; Kopera, M.; Constantinescu, E.; Suckale, J.; Giraldo, F. A continuous/discontinuous Galerkin solution of the shallow water equations with dynamic viscosity, high-order wetting and drying, and implicit time integration, 2016 (arXiv preprint) | arXiv

[9] Nazarov, M. Convergence of a residual based artificial viscosity finite element method, Comput. Math. Appl., Volume 65 (2013) no. 4, pp. 616-626

[10] Nazarov, M.; Larcher, A. Numerical investigation of a viscous regularization of the Euler equations by entropy viscosity, Comput. Methods Appl. Mech. Eng., Volume 317 (2017), pp. 128-152

[11] Patera, A. A spectral element method for fluid dynamics: laminar flow in a channel expansion, J. Comput. Phys., Volume 54 (1984) no. 3, pp. 468-488

[12] Persson, P.; Peraire, J. Sub-cell shock capturing for discontinuous Galerkin methods, Reno, NV, USA, 9–12 January (2006), p. 112 | DOI

Cité par Sources :