Free Access
Issue
ESAIM: M2AN
Volume 50, Number 1, January-February 2016
Page(s) 187 - 214
DOI https://doi.org/10.1051/m2an/2015037
Published online 14 January 2016
  1. I. Babuška, The finite element method with Lagrangian multipliers. Numer. Math. 20 (1973) 179–192. [CrossRef] [Google Scholar]
  2. A.L. Bauer, D.E. Burton, E.J. Caramana, R. Loubère, M.J. Shashkov and P.P. Whalen, The internal consistency, stability, and accuracy of the discrete, compatible formulation of Lagrangian hydrodynamics. J. Comput. Phys. 218 (2006) 572–593. [CrossRef] [Google Scholar]
  3. F. Ben Belgacem, The mortar finite element method with Lagrange multipliers. Numer. Math. 84 (1999) 173–199. [CrossRef] [MathSciNet] [Google Scholar]
  4. D.J. Benson, Computational methods in Lagrangian and Eulerian hydrocodes. Comput. Meth. Appl. Mech. Engrg. 99 (1992) 235–394. [Google Scholar]
  5. C. Bernardi, Y. Maday and A.T. Patera, A New Nonconforming Approach to Domain Decomposition: The Mortar Element Method. Nonlin. Partial Differ. Equ. Appl. Edited by H. Brezis and J. L. Lions. Pitman, New York (1994) 13–51. [Google Scholar]
  6. N.G. Bourago and V.N. Kukudzhanov, A Review of Contact Algorithms. The Institute for Problems in Mechanics of RAS. Izv. RAN, MTT Translation into english (2005) 45–87. [Google Scholar]
  7. J.P. Braeunig, B. Desjardin and J.M. Ghidaglia, A totally Eulerian finite volume solver for multi-material fluid flows. Eur. J. Mech. B/Fluids 28 (2009) 475–485. [CrossRef] [MathSciNet] [Google Scholar]
  8. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Springer−Verlag, New York (1991). [Google Scholar]
  9. F. Brezzi and L.D. Marini, Macro Hybrid Elements and Domain Decomposition Methods. In Vol. 89 of Optimisation et Contrôle, Meeting in honour of J. Céa, edited by J.D. et al. CÉPADUÈS-Edition, Toulouse (1993) (1992). [Google Scholar]
  10. E.J. Caramana, The implementation of slide lines as a combined force and velocity boundary condition. J. Comput. Phys. 228 (2009) 3911–3916. [CrossRef] [Google Scholar]
  11. E.J. Caramana, D.E. Burton, M.J. Shashkov and P.P. Whalen, The construction of compatible hydrodynamics algorithms utilizing conservation of total energy. J. Comput. Phys. 146 (1998) 227–262. [CrossRef] [Google Scholar]
  12. G. Carré, S. Del Pino, B. Després and E. Labourasse, A cell-centered Lagrangian hydrodynamics scheme in arbitrary dimension. J. Comput. Phys. 228 (2009) 5160–5183. [CrossRef] [Google Scholar]
  13. G. Clair, B. Després and E. Labourasse, A one-mesh method for the cell-centered discretization of sliding. Comput. Meth. Appl. Mech. Engrg. 269 (2014) 315–333. [CrossRef] [Google Scholar]
  14. A. Claisse, P. Rouzier and J.M. Ghidaglia, A 2D Sliding Algorithm for Eulerian Multimaterial Simulations. In ECCOMAS 6th European Congress on Computational Methods in Applied Sciences and Engineering (2012). [Google Scholar]
  15. S. Del Pino, A curvilinear finite-volume method to solve compressible gas dynamics in semi-Lagrangian coordinates. C. R. Acad. Sci. Paris, Ser. I 348 (2010) 1027–1032. [CrossRef] [Google Scholar]
  16. B. Després and E. Labourasse, Stabilization of cell-centered compressible Lagrangian methods using subzonal entropy. J. Comput. Phys. 231 (2012) 6559–6595. [CrossRef] [Google Scholar]
  17. B. Després and C. Mazeran, Lagrangian gas dynamics in two dimensions and Lagrangian systems. Arch. Rational Mech. Anal. 178 (2005) 327–372. [CrossRef] [MathSciNet] [Google Scholar]
  18. V. Dyadeshko and M. Shashkov, Reconstruction of multi-material interfaces from moment data. J. Comput. Phys. 227 5361–5384 (2008) [CrossRef] [Google Scholar]
  19. J.M. Escobar, E. Rodríguez, R. Motenegro and G.M. Montero, G.Y.J., Simultaneous untangling and smoothing of tetrahedral meshes. Comput. Meth. Appl. Mech. Engrg. 192 (2003) 2775–2787. [CrossRef] [Google Scholar]
  20. G. Folzan, Modélisation multi-matériaux multi-vitesse en dynamique rapide. Under the direction of P. Le Tallec and J.-P. Perlat (in french). Ph.D. thesis, École Poytechnique (2013). [Google Scholar]
  21. G.H. Golub and C.F. Van Loan, Matrix Computations, 3rd edition. John Hopkins University Press (1996). [Google Scholar]
  22. C.W. Hirt and B.D. Nichols, Volume Of Fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39 (1981) 201–225. [CrossRef] [Google Scholar]
  23. B.I. Jun, A modified equipotential method for grid relaxation. Tech. Rep. UCRL-JC-138277. Lawrence Livermore National Laboratory (2000) [Google Scholar]
  24. M. Kucharik, R. Loubère, L. Bednárik and R. Liska, Enhancement of Lagrangian Slide Lines as a Combined for and Velocity Boundary Condition. Comput. Fluids (2012). [Google Scholar]
  25. X.S. Li, An Overview of SuperLU: Algorithms, Implementation and User Interface. In Vol. 31 (2005) 302–325. [Google Scholar]
  26. P.H. Maire, R. Abgrall, J. Breil and J. Ovadia, A cell-centered Lagrangian scheme for two-dimensional compressible flow problems. SIAM J. Sci. Comput. 29 (2007) 1781–1824. [CrossRef] [Google Scholar]
  27. C. Mazeran, Sur la structure mathématique et l’approximation numérique de l’hydrodynamique Lagrangienne bidimensionelle. Under the direction of B. Després (in french). Ph.D. thesis, Université Bordeaux I (2007). [Google Scholar]
  28. N.R. Morgan, M.A. Kenamond, D.E. Burton, T.C. Carney and D.J. Ingraham, An approach for treating contact surfaces in Lagrangian cell-centered hydrodynamics. J. Comput. Phys. 250 (2013) 527–554. http://dx.doi.org/10.1016/j.jcp.2013.05.015. http://www.sciencedirect.com/science/article/pii/S002199911300346X [CrossRef] [Google Scholar]
  29. J. von Neumann and R.D. Richtmyer, A method for the calculation of hydrodynamics shocks. J. Appl. Phys. 21 (1950) 232–237. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  30. O. Steinbach, On a generalized L2 projection and some related stability estimates in Sobolev spaces. Numer. Math. 90 (2002) 775–786. [CrossRef] [MathSciNet] [Google Scholar]
  31. R. Tipton, Grid optimization by equipotential relaxation. Unpublished manuscript (1990). [Google Scholar]
  32. M.L. Wilkins, Calculation of Elastic-Plastic Flow. In Vol. 3 of Meth. Comput. Phys. Academic Press (1964) 211–263. [Google Scholar]
  33. D.L. Youngs, Time dependent Multi-Material Flow with Large Fluid Distortion. In Numer. Methods Fluid Dyn. Edited by K.W. Morton, M.J. Baines (1982) 273–285 [Google Scholar]
  34. Y.B. Zel’dovich and Y.P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena. Vol. 1. Academic Press, New York and London (1966). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you