zbMATH — the first resource for mathematics

Enhancement of Lagrangian slide lines as a combined force and velocity boundary condition. (English) Zbl 1290.76137
Summary: Many hydrodynamical problems involve shear flows along material interfaces. If the materials move along each other but are tied to a single Lagrangian computational mesh without any sliding treatment, severe mesh distortions appear which can eventually cause the failure of the simulation. This problem is usually treated by introducing the sliding line framework into the Lagrangian code. In this paper, we revise the 2D approach described in [E. J. Caramana, J. Comput. Phys. 228, No. 11, 3911–3916 (2009; Zbl 1273.76258)], and suggest two enhancements – interpolated interaction instead of a simple one-to-one interaction described in the previous article, and a numerical surface tension model improving the stability of the interface. Both improvements stabilize the slide line and lead to more realistic results, as shown on selected numerical examples.

76N15 Gas dynamics (general theory)
Full Text: DOI
[1] Limpouch, J.; Liska, R.; Kuchařík, M.; Váchal, P.; Kmetík, V., Laser-driven collimated plasma flows studied via ALE code, (37th EPS conference on plasma physics, (2010), European Physical Society), P4.22, ISBN 2-914771-62-2
[2] Kuchařík, M.; Liska, R.; Limpouch, J.; Váchal, P., ALE simulations of high-velocity impact problem, Czech J Phys, 54, Suppl. C, 391-396, (2004)
[3] (Zukas, Jonas A., Introduction to hydrocodes, Studies in applied mechanics, vol. 49, (2004), Elsevier) · Zbl 1058.74007
[4] Benson, D. J., Computational methods in Lagrangian and Eulerian hydrocodes, Comput Methods Appl Mech Eng, 99, 2-3, 235-394, (1992) · Zbl 0763.73052
[5] Wriggers, P., Computational contact mechanics, (2006), Springer-Verlag, ISBN 10 3-540-32608-1 · Zbl 1104.74002
[6] Zywicz, E.; Puso, M. A., A general conjugate-gradient-based predictor-corrector solver for explicit finite-element contact, Int J Numer Methods Eng, 44, 4, 439-459, (1999) · Zbl 0949.74074
[7] Weyler, R.; Oliver, J.; Sain, T.; Cante, J. C., On the contact domain method: a comparison of penalty and Lagrange multiplier implementations, Comput Methods Appl Mech Eng, 205-208, 68-82, (2012) · Zbl 1239.74075
[8] Wilkins ML. Calculation of elastic-plastic flow. Technical report UCRL-7322, California. Univ., Livermore, Lawrence Radiation Lab.; 1963.
[9] Wilkins, M. L., Computer simulation of dynamic phenomena, Scientific computation, (1999), Springer
[10] Burton, D. E., Advances in the free-Lagrange method including contributions on adaptive gridding and the smooth particle hydrodynamics method, (Lecture notes in physics, vol. 395, (1991), Springer), 267-276, [Chapter Free-Lagrange Advection Slide Lines], ISBN 978-3-540-54960-4
[11] Barlow, A. J.; Whittle, J., Mesh adaptivity and material interface algorithms in a two dimensional Lagrangian hydrocode, Chem Phys Rep, 19, 2, 15-26, (2000)
[12] Dawes, A. S., A three-dimensional contact algorithm for sliding surfaces, Int J Numer Methods Fluids, 42, 11, 1189-1210, (2003) · Zbl 1030.76027
[13] Bourago, N. G., A survey on contact algorithms, (Ivanenko, S. A.; Garanzha, V. A., Proceedings of workshop grid generation: theory and applications, (2002), Computing Centre of RAS Moscow)
[14] Caramana, E. J.; Burton, D. E.; Shashkov, M. J.; Whalen, P. P., The construction of compatible hydrodynamics algorithms utilizing conservation of total energy, J Comput Phys, 146, 1, 227-262, (1998) · Zbl 0931.76080
[15] Caramana, E. J., The implementation of slide lines as a combined force and velocity boundary condition, J Comput Phys, 228, 11, 3911-3916, (2009) · Zbl 1273.76258
[16] Caramana, E. J.; Shashkov, M. J.; Whalen, P. P., Formulations of artificial viscosity for muti-dimensional shock wave computations, J Comput Phys, 144, 2, 70-97, (1998) · Zbl 1392.76041
[17] Caramana, E. J.; Shashkov, M. J., Elimination of artificial grid distortion and hourglass-type motions by means of Lagrangian subzonal masses and pressures, J Comput Phys, 142, 2, 521-561, (1998) · Zbl 0932.76068
[18] Carpenter, N. J.; Taylor, R. L.; Katona, M. G., Lagrange constraints for transient finite element surface contact, Int J Numer Methods Eng, 32, 1, 103-128, (1991) · Zbl 0763.73053
[19] Hallquist, J. O.; Goudreau, G. L.; Benson, D. J., Sliding interfaces with contact-impact in large-scale Lagrangian computations, Comput Methods Appl Mech Eng, 51, 1-3, 107-137, (1985) · Zbl 0567.73120
[20] Zhong ZH. On contact-impact problems. PhD thesis, Linkoping University, Linkoping, Sweden; 1988.
[21] Weseloh WN, Clancy SP, Painter JW. PAGOSA physics manual. Technical report. Los Alamos National Laboratory; 2010 [LA-14425-M].
[22] ABAQUS 6.10 Analysis User Manual, vol. V. Dassault Systemes; 2010.
[23] Francois, M. M.; Cummins, S. J.; Dendy, E. D.; Kothe, D. B.; Sicilian, J. M.; Williams, M. W., A balanced-force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework, J Comput Phys, 213, 1, 141-173, (2006) · Zbl 1137.76465
[24] Dobrev, V. A.; Ellis, T. E.; Kolev, Tz. V.; Rieben, R. N., Curvilinear finite elements for Lagrangian hydrodynamics, Int J Numer Methods Fluids, 65, 11-12, 1295-1310, (2011) · Zbl 1255.76075
[25] Badziak, J.; Borodziuk, S.; Pisarczyk, T.; Chodukowski, T.; Krousky, E.; Masek, K.; Skala, J.; Ullschmied, J.; Rhee, Y.-J., Highly efficient acceleration and collimation of high-density plasma using laser-induced cavity pressure, Appl Phys Lett, 96, 25, 251-502, (2010)
[26] Galera, S.; Maire, P.-H.; Breil, J., A two-dimensional unstructured cell-centered multi-material ALE scheme using VOF interface reconstruction, J Comput Phys, 229, 16, 5755-5787, (2010) · Zbl 1346.76105
[27] Loubère, R.; Caramana, E. J., The force/work differencing of exceptional points in the discrete compatible formulation of Lagrangian hydrodynamics, J Comput Phys, 216, 1, 1-18, (2006) · Zbl 1173.76389
[28] Fung J, Francois M, Dendy E, Kenamond M, Lowrie R. Calculations of the Rayleigh-Taylor instability: RAGE and FLAG hydrocode comparisons. In: Proceedings of NECDC06; 2006.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.