Free Access
Issue |
ESAIM: M2AN
Volume 50, Number 1, January-February 2016
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Page(s) | 187 - 214 | |
DOI | https://doi.org/10.1051/m2an/2015037 | |
Published online | 14 January 2016 |
- I. Babuška, The finite element method with Lagrangian multipliers. Numer. Math. 20 (1973) 179–192. [CrossRef] [Google Scholar]
- 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]
- F. Ben Belgacem, The mortar finite element method with Lagrange multipliers. Numer. Math. 84 (1999) 173–199. [CrossRef] [MathSciNet] [Google Scholar]
- D.J. Benson, Computational methods in Lagrangian and Eulerian hydrocodes. Comput. Meth. Appl. Mech. Engrg. 99 (1992) 235–394. [Google Scholar]
- 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]
- 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]
- 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]
- F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Springer−Verlag, New York (1991). [Google Scholar]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- V. Dyadeshko and M. Shashkov, Reconstruction of multi-material interfaces from moment data. J. Comput. Phys. 227 5361–5384 (2008) [CrossRef] [Google Scholar]
- 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]
- 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]
- G.H. Golub and C.F. Van Loan, Matrix Computations, 3rd edition. John Hopkins University Press (1996). [Google Scholar]
- 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]
- B.I. Jun, A modified equipotential method for grid relaxation. Tech. Rep. UCRL-JC-138277. Lawrence Livermore National Laboratory (2000) [Google Scholar]
- 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]
- X.S. Li, An Overview of SuperLU: Algorithms, Implementation and User Interface. In Vol. 31 (2005) 302–325. [Google Scholar]
- 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]
- 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]
- 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]
- 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]
- 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]
- R. Tipton, Grid optimization by equipotential relaxation. Unpublished manuscript (1990). [Google Scholar]
- M.L. Wilkins, Calculation of Elastic-Plastic Flow. In Vol. 3 of Meth. Comput. Phys. Academic Press (1964) 211–263. [Google Scholar]
- 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]
- 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]
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