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A new method to introduce constraints in cell-centered Lagrangian schemes. (English) Zbl 1286.76111
Summary: We describe a new method to introduce constraints in cell-centered Lagrangian schemes in the framework of compressible hydrodynamics. In this paper we apply it to the modeling of contact and sliding on solid wall boundaries. We illustrate our method, which is based on the minimization of a specific objective function, by several basic problems.

76M25 Other numerical methods (fluid mechanics) (MSC2010)
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
76N15 Gas dynamics (general theory)
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[1] L.D. Lifschitz, E.M. Landau, Fluid Mechanics, Course of Theoretical physics, vol. 6, second ed., 2010.
[2] Liepmann, H. W.; Roshko, A., Elements of gasdynamics, (2003), Dover Publications Inc. · Zbl 0078.39901
[3] Burago, N. G.; Kukudzhanov, V. N., Mech. Solids, 40, 1, 35-71, (2005)
[4] S. Bertoluzza, S. Del Pino, E. Labourasse, A Conservative slide line method for Cell-Centered semi-lagrangian and ALE shemes in 2D, Journal of Scientific Computing (2013), submitted for publication. · Zbl 1382.76181
[5] Maire, P.-H., J. Comput. Phys., 228, 7, 2391-2425, (2009)
[6] Hallquist, J. O.; Goudreau, G. L.; Benson, D. J., Comput. Meth. Appl. Mech. Engrg., 51, 1-3, 107-137, (1985)
[7] Hallquist, J. O., Report UCRL 52066, (1976), Lawrence Livermore Laboratory Livermore, CA
[8] Attaway, S. W.; Hendrickson, B. A.; Plimpton, S. J.; Gardner, D. R.; Vaughan, C. T.; Brown, K. H.; Heinstein, M. W., Comput. Mech., 22, 143-159, (1998)
[9] Plimpton, S. J.; Attaway, S.; Hendrickson, B.; Swegle, J.; Vaughan, C.; Gardner, D., J. Parallel Distrib. Comput., 50, 104-122, (1998)
[10] Brown, K.; Attaway, S.; Plimpton, S. J.; Hendrickson, B., Comput. Meth. Appl. Mech. Engrg., 184, 375-390, (2000)
[11] González, J. A.; Park, K. C.; Felippa, C. A.; Abascal, R., Comput. Meth. Appl. Mech. Engrg., 197, 6-8, 623-640, (2008)
[12] Tur, M.; Fuenmayor, F. J.; Wriggers, P., Comput. Meth. Appl. Mech. Engrg., 198, 37-40, 2860-2873, (2009)
[13] Weyler, R.; Oliver, J.; Sain, T.; Cante, J. C., Comput. Meth. Appl. Mech. Engrg., 205-208, 68-82, (2012)
[14] Zavarise, G.; De Lorenzis, L., Int. J. Numer. Meth. Engrg., 91, 8, 825-842, (2012)
[15] Ruzzeh, B.; Kvecses, J., J. Comput. Nonlinear Dyn., 6, 2, 1-12, (2011)
[16] Hetherington, J.; Rodriguez-Ferran, A.; Askes, H., Int. J. Numer. Meth. Engrg., 90, 3, 269-286, (2012)
[17] Wilkins, M. L., Computer simulation of dynamic phenomena, (1999), Springer · Zbl 0926.76001
[18] Caramana, E. J., J. Comput. Phys., 228, 3911-3916, (2009)
[19] M. Kucharı́k, R. Loubère b, L. Bednárik, R. Liska, to be published in, Computers & Fluids (2012).
[20] Carré, G.; Del Pino, S.; Després, B.; Labourasse, E., J. Comput. Phys., 228, 5160-5183, (2009)
[21] Glowinski, R.; Lichnewsky, A., Computing methods in applied sciences and engineering, (1991), Society for Industrial & Applied Mathematics US
[22] Allaire, G., Numerical analysis and optimization: an introduction to mathematical modelling and numerical simulation, (2007), OUP Oxford · Zbl 1120.65001
[23] Gehmeyr, M.; Cheng, B.; Mihalas, D., Shock Waves, 7, 255-274, (1997) · Zbl 0909.76042
[24] Wriggers, P., Computational contact mechanics, (2002), Wiley
[25] Stronge, W. J., Impact mechanics, (2004), Cambridge University Press · Zbl 0961.74002
[26] Després, B.; Mazeran, C., Lagrangian gas dynamics in 2D and Lagrangian systems, Arch. Ration. Mech. Anal., 178, (2005) · Zbl 1096.76046
[27] Arrow, K.; Hurwicz, L.; Uzawa, H., Studies in nonlinear programming, (1958), Stanford university press
[28] Bacuta, C., A unified approach for Uzawa algorithms, SIAM J. Numer. Anal., 44, 6, 2633-2649, (2006) · Zbl 1128.76052
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