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Mass matrix formulation of the FLIP particle-in-cell method. (English) Zbl 0761.73117
Summary: A refinement of FLIP [J. U. Brackbill and H. M. Ruppel, J. Comput. Phys. 65, 314-343 (1986; Zbl 0592.76090)] is described which uses a mass matrix formulation to achieve greater accuracy and less numerical diffusion over the previous version. Without the refinement, there is a significant dissipation of energy in modeling elastic vibrations of a solid. Moreover, in modeling an initial flow discontinuity there are sub- grid-scale oscillations in the particle velocity field in the neighborhood of the discontinuity. These difficulties are eliminated using the mass matrix. In addition, the mass matrix formulation conserves kinetic energy, linear and angular momentum, and is Galilean invariant.

74S30 Other numerical methods in solid mechanics (MSC2010)
74H45 Vibrations in dynamical problems in solid mechanics
Full Text: DOI
[1] Brackbill, J.U., J. comput. phys., 96, 163, (1991)
[2] Brackbill, J.U.; Kothe, D.B.; Ruppel, H.M., Comput. phys. commun., 48, 25, (1988)
[3] Brackbill, J.U., Comput. phys. commun., 47, 1, (1987)
[4] Brackbill, J.U., J. comput. phys., 75, 469, (1988)
[5] Sulsky, D.; Brackbill, J.U., J. comput. phys., 96, 339, (1991)
[6] Sulsky, D.; Chen, Z.; Schreyer, H.L., SAND91-7095, sandia national laboratories, albuquerque, NM, (1992)
[7] Peter J. O’Rourke, J. U. Brackbill, and Bernard Larraturou, submitted for publication.
[8] Sod, G.A., J. comput. phys., 27, 1, (1978)
[9] Gilbert, Strang, Introduction to applied mathematics, (), 52 · Zbl 0618.00015
[10] Eastwood, J.W., Comput. phys. commun., 44, 73, (1987)
[11] Brackbill, J.U.; Ruppel, H.M., J. comput. phys., 65, 314, (1986)
[12] Birdsall, C.K.; Langdon, A.B., Plasma physics via computer simulation, (1985), McGraw-Hill New York
[13] Monaghan, J.J., Comput. phys. rep., 3, 71, (1985)
[14] Goad, W.B., LAMS-2365, los alamos national laboratory, los alamos, NM, (1960)
[15] Wilkins, M.L., J. comput. phys., 35, 281, (1980)
[16] von Neumann, J.; Richtmyer, R.D., J. appl. phys., 21, 232, (1950)
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