Comptes Rendus
no. 2
Numerical analysis
High-order accurate Lagrange-remap hydrodynamic schemes on staggered Cartesian grids
[Schémas hydrodynamiques d'ordre très élevé Lagrange-projection sur grilles cartésiennes décalées]

Présenté par : the Editorial Board

Gautier Dakin1 ; Hervé Jourdren1
1 CEA, DAM, DIF, 91297 Arpajon, France
Comptes Rendus. Mathématique, Volume 354 (2016) no. 2, pp. 211-217.

Nous considérons une classe de schémas sur maillage décalé pour résoudre les équations d'Euler 1D. Les schémas proposés, formulés en énergie interne, sont d'ordre élevé en espace comme en temps, utilisables quelle que soit l'équation d'état. En ajoutant une discrétisation de l'équation de l'énergie cinétique, une procédure de synchronisation de l'énergie cinétique est introduite, préservant globalement l'énergie totale et permettant la capture correcte des chocs. Une extension nD sur grille cartésienne décalée de type C avec splitting directionnel d'ordre élevé est proposée. Des résultats numériques sont présentés jusqu'à l'ordre 8.

We consider a class of staggered grid schemes for solving the 1D Euler equations in internal energy formulation. The proposed schemes are applicable to arbitrary equations of state and high-order accurate in both space and time on smooth flows. Adding a discretization of the kinetic energy equation, a high-order kinetic energy synchronization procedure is introduced, preserving globally total energy and enabling proper shock capturing. Extension to nD Cartesian grids is done via C-type staggering and high-order dimensional splitting. Numerical results are provided up to 8th-order accuracy.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.11.008
Gautier Dakin 1 ; Hervé Jourdren 1

1 CEA, DAM, DIF, 91297 Arpajon, France 
@article{CRMATH_2016__354_2_211_0,
     author = {Gautier Dakin and Herv\'e Jourdren},
     title = {High-order accurate {Lagrange-remap} hydrodynamic schemes on staggered {Cartesian} grids},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {211--217},
     publisher = {Elsevier},
     volume = {354},
     number = {2},
     year = {2016},
     doi = {10.1016/j.crma.2015.11.008},
     language = {en},
}
TY  - JOUR
AU  - Gautier Dakin
AU  - Hervé Jourdren
TI  - High-order accurate Lagrange-remap hydrodynamic schemes on staggered Cartesian grids
JO  - Comptes Rendus. Mathématique
PY  - 2016
SP  - 211
EP  - 217
VL  - 354
IS  - 2
PB  - Elsevier
DO  - 10.1016/j.crma.2015.11.008
LA  - en
ID  - CRMATH_2016__354_2_211_0
ER  - 
%0 Journal Article
%A Gautier Dakin
%A Hervé Jourdren
%T High-order accurate Lagrange-remap hydrodynamic schemes on staggered Cartesian grids
%J Comptes Rendus. Mathématique
%D 2016
%P 211-217
%V 354
%N 2
%I Elsevier
%R 10.1016/j.crma.2015.11.008
%G en
%F CRMATH_2016__354_2_211_0
Gautier Dakin; Hervé Jourdren. High-order accurate Lagrange-remap hydrodynamic schemes on staggered Cartesian grids. Comptes Rendus. Mathématique, Volume 354 (2016) no. 2, pp. 211-217. doi : 10.1016/j.crma.2015.11.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.11.008/

[1] A.W. Cook; W.H. Cabot Hyperviscosity for shock-turbulence interactions, J. Comput. Phys., Volume 203 (2005), pp. 379-385

[2] R.B. DeBar Fundamentals of the KRAKEN code, 1974 (Lawrence Livermore Laboratory Report, Technical Report UCIR-760)

[3] S. Del Pino; B. Desprès; P. Havé; H. Jourdren; P.F. Piserchia 3D finite volume simulation of acoustic waves in the Earth atmosphere, Comput. Fluids, Volume 38 (2009) no. 4, pp. 765-777

[4] F. Duboc; C. Enaux; S. Jaouen; H. Jourdren; M. Wolff High-order dimensionally split Lagrange-remap schemes for compressible hydrodynamics, C. R. Acad. Sci. Paris, Ser. I, Volume 348 (2010), pp. 105-110

[5] O. Heuzé; S. Jaouen; H. Jourdren Dissipative issue of high-order shock capturing schemes with non-convex equations of state, J. Comput. Phys., Volume 228 (2009), pp. 833-860

[6] H. Jourdren (LNCSE), Volume vol. 41, Springer (2005), pp. 283-294

[7] W.F. Noh Numerical methods in hydrodynamic calculations, 1976 (Lawrence Livermore Laboratory Report, Technical Report UCRL-52112)

[8] Y.P. Popov; A.A. Samarskii Completely conservative difference schemes, Zh. Vychisl. Mat. Mat. Fiz., Volume 9 (1969) no. 4, pp. 953-958

[9] R.D. Richtmyer Proposed numerical method for calculation of shocks, 1948 (Los Alamos Report, 671)

[10] C.-W. Shu; S. Osher Efficient implementation of essentially non-oscillatory shock-capturing schemes, II, J. Comput. Phys., Volume 83 (1989), pp. 32-78

[11] W.G. Sutcliffe BBC hydrodynamics, 1974 (Lawrence Livermore Laboratory Report, Technical Report UCID-17013)

[12] J.G. Trulio; K.R. Trigger Numerical solution of the one dimensional Lagrangian hydrodynamics equations, 1961 (Lawrence Radiation Laboratory Report, Technical Report UCRL-6267)

[13] J.H. Verner Jim Verner's Refuge for Runge–Kutta pairs, 2013 http://people.math.sfu.ca/~jverner/

[14] J. von Neumann; R.D. Richtmyer A method for numerical calculation of hydrodynamic shocks, J. Appl. Phys., Volume 21 (1950), pp. 232-237

[15] P. Woodward; P. Colella The numerical simulation of two-dimensional fluid flow with strong shocks, J. Comput. Phys., Volume 54 (1984), pp. 115-173

[16] H. Yoshida Construction of higher order symplectic integrators, Phys. Lett. A, Volume 150 (1990), pp. 262-267

[17] D.L. Youngs The Lagrangian remap method, Implicit Large Eddy Simulation: Computing Turbulent Flow Dynamics, Cambridge University Press, Cambridge, UK, 2007

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

High-order dimensionally split Lagrange-remap schemes for compressible hydrodynamics

Frédéric Duboc; Cédric Enaux; Stéphane Jaouen; ...

C. R. Math (2010)

Preliminary evidence for associations between molecular markers and quantitative traits in a set of bread wheat (Triticum aestivum L.) cultivars and breeding lines

Babak Abdollahi Mandoulakani; Shilan Nasri; Sahar Dashchi; ...

C. R. Biol (2017)