A comparative study of two different numerical schemes for the simulation of nonlinear dynamics of heated falling thin films
In this research, an attempt is made to characterise qualitatively the stability and dynamics of an inclined thin liquid film under the influence of instabilities due to thermo-capillarity and evaporative effects as well as van der Waals intermolecular forces, by employing the implicit finite di...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English English |
| Published: |
Blue Eyes Intelligence Engineering and Sciences Publication
2019
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/73648/ http://irep.iium.edu.my/73648/ http://irep.iium.edu.my/73648/1/73648_A%20Comparative%20Study%20of%20Two_article.pdf http://irep.iium.edu.my/73648/2/73648_A%20Comparative%20Study%20of%20Two_scopus.pdf |
| Summary: | In this research, an attempt is made to characterise
qualitatively the stability and dynamics of an inclined thin liquid
film under the influence of instabilities due to thermo-capillarity
and evaporative effects as well as van der Waals intermolecular
forces, by employing the implicit finite difference method. The
results are compared with solutions obtained by the Fourier
spectral method. Flow in thin films of a Newtonian liquid on an
inclined plane with an adjacent passive gas layer, is well
represented by the Navier-Stokes equations, equation of
continuity and associated boundary conditions. Long-wave
(lubrication) approximation is applied to simplify the governing
equations to arrive at a nonlinear partial differential equation,
called equation of evolution (EOE). The spatio-temporal
evolution of the interfacial instability in the film caused by
internal and/or external effects are studied by numerically solving
the EOE using the implicit finite difference method. The results of
the numerical simulations of our thin film model are compared
with those of a similar problem solved using Fourier spectral
method from the literature. Simulations show remarkable
agreement in the film dynamics predicted by these two methods.
The film rupture times obtained using our implicit finite
difference scheme closely match with the values obtained from
the Fourier spectral method within less than 1% error. This
implies that the implicit finite difference method can be
satisfactorily employed for the efficient numerical simulation of
the thin film flows, and to decipher its nonlinear dynamics
reliably. |
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