An Implicit Finite Difference Method for Thin Film Flow

Gusrian Putra; Leo Hari Wiryanto; Ratna Widyawati

doi:10.22342/jims.29.1.1110.99-105

Gusrian Putra ⁽¹⁾ , Leo Hari Wiryanto ⁽²⁾ , Ratna Widyawati ⁽³⁾

(1) Department of Sciences, Institut Teknologi Sumatera, Indonesia,

(2) Department of Mathematics, Institut Teknologi Bandung, Indonesia,

(3) Department of Civil Engineering, University of Lampung, Indonesia

https://doi.org/10.22342/jims.29.1.1110.99-105

Issue
VOLUME 29 NUMBER 1 (MARCH 2023)

Submitted
December 8, 2021

Accepted
January 3, 2023

Published
March 30, 2023

Keywords:

thin film flow, theory of lubrication, single equation, numerical wave-simulation

PDF

Abstract

Thin film flow on an inclined plane can be modeled from lubrication theory. Together with boundary
conditions, the governing equations can be formulated into a single equation of the thickness of the
fluid, and solved numerically by an implicit finite difference method. In analyzing the equation,
the linearized equation is considered here, to see the characteristic of the solution as wave propagation
and the effect of the physical parameter. We found that the wave propagates by reducing the amplitude,
and the wave speed is affected by the steepness of the plane. All of these can be indicated in the
linearized equation. Numerical wave-simulation is presented in this paper.

Full text article

Generated from XML file

References

Wiryanto, L. H. and Febrianti, W, ”Numerical solution of thin-film flowing down on an inclined channel”, Adv. Appl. Fluid Mech., 20 (2017), 595-604

Wiryanto, L. H, ”Stability analysis of thin film model”, Journal of Physics: Conf. Series, 983 (2018), 012072

Wiryanto, L. H, ”A finite difference method for a thin film model”, Proc. Int. Conf. on mechanical, electrical and medical intelligent system (ICMEMIS) (2017), GS-02

King, C., Tuck, E. O. and Vanden J.M, ”Air-blown on thin viscous sheets”, Phys. Fluids A, 5 (1993), 973-978

Needham, D. J. and Merkin, J.H, ”On roll waves down an open inclined channel”, Proc. R. Soc. Lond. A, 394 (1984), 259-278.

Merkin, J. H. and Needham, D. J, ”An infinite periodic bifurcation arising in roll waves down an open inclined channel”, Proc. R. Soc. London Ser. A, 405 (1986), 103-116

Fauzi, R. and Wiryanto L. H, ”On the staggered scheme for shallow water model down an inclined channel”, AIP Conf. Proc. 1867 (2017)

Fauzi, R. and Wiryanto L. H, ”Predictor-corrector scheme for simulating wave propagation on shallow water region”, IOP Conf. Ser.: Earth Environ. Sci, 162 (2018), 012047

Dressler, R. F, ”Mathematical solution of problem of roll-waves in open inclined channels”, Commun. Pure Appl. Math, 2 (1949), 149-194.

Wiryanto, L.H., Widyawati, R., Fauzi, R., Putra, G., Noviani, E., ”Simulation of wave propagation on thin film”, Adv. Appl. Fluid Mech., 2022, 29 (2022), 45-58

Authors

Gusrian Putra

Department of Sciences, Institut Teknologi Sumatera

Leo Hari Wiryanto

Department of Mathematics, Institut Teknologi Bandung

leo@math.itb.ac.id (Primary Contact)

Ratna Widyawati

Department of Civil Engineering, University of Lampung

Putra, G., Wiryanto, L. H., & Widyawati, R. (2023). An Implicit Finite Difference Method for Thin Film Flow. Journal of the Indonesian Mathematical Society, 29(1), 99–105. https://doi.org/10.22342/jims.29.1.1110.99-105