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Hutchinson, A. J.; Harley, C.; Momoniat, E.

Numerical investigation of the steady state of a driven thin film equation. (English) Zbl 1266.76009

J. Appl. Math. 2013, Article ID 181939, 6 p. (2013).
Summary: A third-order ordinary differential equation with application in the flow of a thin liquid film is considered. The boundary conditions come from Tanner’s problem for the surface tension driven flow of a thin film. Symmetric and nonsymmetric finite difference schemes are implemented in order to obtain steady state solutions. We show that a central difference approximation to the third derivative in the model equation produces a solution curve with oscillations. A difference scheme based on a combination of forward and backward differences produces a smooth accurate solution curve. The stability of these schemes is analysed through the use of a von Neumann stability analysis.

MSC:

76A20 Thin fluid films
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\textit{A. J. Hutchinson} et al., J. Appl. Math. 2013, Article ID 181939, 6 p. (2013; Zbl 1266.76009)
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References:

[1] A. L. Bertozzi, A. Münch, and M. Shearer, “Undercompressive shocks in thin film flows,” Physica D, vol. 134, no. 4, pp. 431-464, 1999. · Zbl 1076.76509
[2] E. Momoniat, “A nonlinear eigenvalue problem from thin-film flow,” Journal of Engineering Mathematics, 2012. · Zbl 1288.76011
[3] L. H. Tanner, “The spreading of silicone oil drops on horizontal surfaces,” Journal of Physics D, vol. 12, pp. 1473-1484, 1979.
[4] E. Momoniat, “Numerical investigation of a third-order ODE from thin film flow,” Meccanica, vol. 46, no. 2, pp. 313-323, 2011. · Zbl 1271.76215
[5] A. L. Bertozzi, “Symmetric singularity formation in lubrication-type equations for interface motion,” SIAM Journal on Applied Mathematics, vol. 56, no. 3, pp. 681-714, 1996. · Zbl 0856.35002
[6] A. L. Bertozzi, “The mathematics of moving contact lines in thin liquid films,” Notices of the American Mathematical Society, vol. 45, no. 6, pp. 689-697, 1998. · Zbl 0917.35100
[7] E. Momoniat, “On the determination of the steady film profile for a non-Newtonian thin droplet,” Computers & Mathematics with Applications, vol. 62, no. 1, pp. 383-391, 2011. · Zbl 1228.76009
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