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Finite difference modeling of solitons induced by a density hump in a plasma multi-fluid. (English) Zbl 0987.76065
Summary: A Lax-Wendroff type semi-implicit numerical scheme is employed to numerically integrate the nonlinear one-dimensional unmagnetized plasma multi-fluid equations for ideal gases to obtain soliton solutions from an initial density hump profile. The time evolution of such solitons is studied and found to be similar to those obtained with previous simulation techniques and to those that have been observed in experimental studies. Effects such as two-soliton collisions and soliton-boundary reflections, are observed by means of a model involving a fully nonlinear time-evolutionary numerical treatment of plasma as a multi-fluid.

76M20 Finite difference methods applied to problems in fluid mechanics
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
Full Text: DOI
[1] Mason, R.J., Computer simulation of ion-acoustic shocks II: slug and piston problems, Phys. fluids, 15, 845-853, (1972)
[2] Cohn, D.B.; MacKenzie, K.R., Density-step-excited ion-acoustic solitons, Phys. rev. lett., 30, 258-261, (1973)
[3] Biskamp, D.; Parkinson, D., Ion-acoustic shock waves, Phys. fluids, 13, 2295-2299, (1970)
[4] Ogino, T.; Takeda, S., Computer simulation and analysis for spherical and cylindrical ion-acoustic solitons, J. phys. soc. jpn., 41, 257-264, (1976)
[5] S. Baboolal, Finite-difference solution of the nonlinear one-dimensional electrostatic plasma multi-fluid equations: solitons and recurrence, in: C. Taylor, (Ed.), Numerical Methods in Laminar and Turbulent Flow, Part 2, Vol. VIII, Pineridge Press, Swansea, 1993, pp. 1599-1610.
[6] Baboolal, S.; Bharuthram, R.; Hellberg, M.A., Arbitrary amplitude theory of ion-acoustic solitons in warm multi-fluid plasmas, J. plasma phys., 41, 341-353, (1989)
[7] A. Jeffrey, Quasilinear Hyperbolic Systems and Waves, Pitman Publishing, London, 1976, p. 42. · Zbl 0322.35060
[8] Harten, A.; Lax, P.D.; Levermore, C.D.; Morokoff, W.J., Convex entropies and hyperbolicity for general Euler equations, SIAM J. numer. anal., 35, 2117-2127, (1998) · Zbl 0922.35089
[9] A.R. Mitchell, D.F. Griffiths, The Finite-Difference Method in Partial Differential Equations, Wiley, Chichester, 1980, p. 175. · Zbl 0417.65048
[10] J.D. Anderson Jr. Computational Fluid Dynamics, McGraw-Hill, New York, 1995, p. 82.
[11] Y. Nakamura, Ion-acoustic solitons in a multi-component plasma with negative ions, in: H. Kikuchi (Ed.), Nonlinear and Environmental Electromagnetics, Elsevier, Amsterdam, 1985, pp. 139-164.
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