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A one-mesh method for the cell-centered discretization of sliding. (English) Zbl 1296.76131
Summary: A new method is described to treat slide lines in cell-centered Lagrangian schemes for the modeling of sliding problems between two fluids in the framework of compressible hydrodynamics. The method is an extension of the one proposed by G. Clair et al. [Comput. Methods Appl. Mech. Eng. 261–262, 56–65 (2013; Zbl 1286.76111)] and is conservative in momentum and total energy. We illustrate our method, which is based on the minimization of an objective function over a specific set that models the sliding constraint, by several basic problems.

MSC:
76N15 Gas dynamics (general theory)
74M15 Contact in solid mechanics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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[1] Clair, G.; Després, B.; Labourasse, E., Comput. Methods Appl. Mech. Eng., 261-262, 56-65, (2013)
[2] Hughes, T. J.R.; Taylor, R. L.; Sackman, J. L.; Curnier, A.; Kanoknukulchai, W., Comput. Methods Appl. Mech. Eng., 8, 3, 249-276, (1976)
[3] Hild, P.; Renard, Y., Numer. Math., 115, 1, 101-129, (2010)
[4] Campos, L. T.; Oden, J. T.; Kikuchi, N., Comput. Methods Appl. Mech. Eng., 34, 1-3, 821-845, (1982)
[5] L. Demkowicz, J.T. Oden, ICES, REPORT 81-13, 1981.
[6] Belgacem, F. B.; Hild, P.; Laborde, P., Math. Comput. Model., 28, 263-271, (1998)
[7] El-Abbasi, N.; Meguid, S. A., Int. J. Numer. Methods Eng., 50, 953-967, (2001)
[8] Refaat, M. H.; Meguid, S. A., Int. J. Numer. Methods Eng., 40, 2975-2993, (1997)
[9] Burago, N. G.; Kukudzhanov, V. N., Mech. Solids, 40, 1, 35-71, (2005)
[10] Wilkins, M. L., Computer simulation of dynamic phenomena, (1999), Springer · Zbl 0926.76001
[11] Burton, D. E., (Lecture Notes in Physics, 395, (1991), Springer), 267-276
[12] Barlow, A. J.; Whittle, J., Chem. Phys. Rep., 19, 2, 15-26, (2000)
[13] Dawes, A. S., Int. J. Numer. Methods Fluids, 42, 11, 1189-1210, (2003)
[14] Caramana, E. J., J. Comput. Phys., 228, 3911-3916, (2009)
[15] Kucharik, M.; Loubere, R.; Bednarik, L.; Liska, R., Comput. Fluids, 83, 3-14, (2013)
[16] Carré, G.; Del Pino, S.; Després, B.; Labourasse, E., J. Comput. Phys., 228, 5160-5183, (2009)
[17] Maire, P.-H., J. Comput. Phys., 228, 7, 2391-2425, (2009)
[18] Benson, D. J., Comput. Methods Appl. Mech. Eng., 99, 2-3, 235-394, (1992)
[19] Morgan, N. R.; Kenamond, M. A.; Burton, D. E.; Carney, T. C.; Ingraham, D. J., J. Comput. Phys., 250, 527-554, (2013)
[20] S. Bertoluzza, S. Del Pino, E. Labourasse, J. Sci. Comput., 2013. submitted for publication.
[21] Després, B.; Mazeran, C., C.R. Mec., 331, (2003)
[22] Loubère, R.; Caramana, E. J., J. Comput. Phys., 216, 1-18, (2006)
[23] Claisse, A.; Després, B.; Labourasse, E.; Ledoux, F., J. Comput. Phys., 231, 11, 4324-4354, (2012)
[24] Glowinski, R.; Lichnewsky, A., Computing methods in applied sciences and engineering, (1991), Society for Industrial & Applied Mathematics US
[25] Allaire, G., Numerical analysis and optimization: an introduction to mathematical modelling and numerical simulation, (2007), OUP, Oxford · Zbl 1120.65001
[26] Laursen, T. A., Computational contact and impact mechanics, (2003), Springer
[27] Wriggers, P., Computational contact mechanics, (2006), Springer · Zbl 1104.74002
[28] Maire, P. H.; Nkonga, B., J. Comput. Phys., 228, 3, 799-821, (2009)
[29] Sod, G. A., J. Comput. Phys., 27, 1-31, (1978)
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