On the numerical solution of a driven thin film equation

Ha, Youngsoo; Kim, Yong-Jung; Myers, T.G.

doi:10.1016/j.jcp.2008.04.007

Cited by 16 publications

(19 citation statements)

References 27 publications

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“…We have shown that the implicit-explicit scheme is more efficient than the Crank-Nicolson scheme. This is an improvement on the work of Ha et al [16]. The finite difference schemes presented in this work are easier to implement than the schemes derived by Zhornitskaya and Bertozzi [29].…”

Section: ð3:14þmentioning

confidence: 72%

“…The finite difference schemes satisfy conservation of mass, conservation of surface energy dissipation and a nonlinear energy dissipation. Ha et al [16] have investigated numerical solutions of (1.1) coupled with a nonlinear source term @/@x(u 2 Àu 3 ). Ha et al [16] solve the nonlinear diffusion term given by (1.1) using a Crank-Nicolson scheme.…”

Section: Introductionmentioning

confidence: 99%

“…Ha et al [16] have investigated numerical solutions of (1.1) coupled with a nonlinear source term @/@x(u 2 Àu 3 ). Ha et al [16] solve the nonlinear diffusion term given by (1.1) using a Crank-Nicolson scheme. In this paper we show that an implicit-explicit scheme is unconditionally stable and is more efficient for solving the nonlinear diffusion Eq.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Numerical investigation of the generalized lubrication equation

Momoniat

Harley

Adlem

2010

Applied Mathematics and Computation

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Section: ð3:14þmentioning

confidence: 72%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Numerical investigation of the generalized lubrication equation

Momoniat

Harley

Adlem

2010

Applied Mathematics and Computation

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“…al. [3] point out that the WENO-JS methods are relatively stable than the other explicit methods. We can see that the other WENO schemes -WENO-Z and WENO-M -are stable.…”

Section: Numerical Resultsmentioning

confidence: 91%

“…For the diffusion equation we are using Crank-Nicolson methods (see [3]). We now consider a numerical scheme for the convection part,…”

Section: Numerical Schemesmentioning

confidence: 99%

Numerical Comparison of Weno Type Schemes to the Simulations of Thin Films

Kang¹,

Kim²,

Ha³

2012

Journal of the Korea Society for Industrial and Applied Mathema

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ABSTRACT. This paper is comparing numerical schemes for a differential equation with convection and fourth-order diffusion. Our model equation is ht + (h 2 − h 3 )x = −(h 3 hxxx)x, which arises in the context of thin film flow driven the competing effects of an induced surface tension gradient and gravity. These films arise in thin coating flows and are of great technical and scientific interest. Here we focus on the several numerical methods to apply the model equation and the comparison and analysis of the numerical results. The convection terms are treated with well known WENO methods and the diffusion term is treated implicitly. The diffusion and convection schemes are combined using a fractional step-splitting method.

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Numerical studies of the fingering phenomena for the thin film equation

Lee

Yoon

et al. 2010

Numerical Methods in Fluids

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SUMMARYWe present a new interpretation of the fingering phenomena of the thin liquid film layer through numerical investigations. The governing partial differential equation is h t +(h 2 −h 3 ) x =−∇ ·(h 3 ∇ h), which arises in the context of thin liquid films driven by a thermal gradient with a counteracting gravitational force, where h = h(x, y, t) is the liquid film height. A robust and accurate finite difference method is developed for the thin liquid film equation. For the advection part (h 2 −h 3 ) x , we use an implicit essentially nonoscillatory (ENO)-type scheme and get a good stability property. For the diffusion part −∇ ·(h 3 ∇ h), we use an implicit Euler's method. The resulting nonlinear discrete system is solved by an efficient nonlinear multigrid method. Numerical experiments indicate that higher the film thickness, the faster the film front evolves. The concave front has higher film thickness than the convex front. Therefore, the concave front has higher speed than the convex front and this leads to the fingering phenomena.

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On the numerical solution of a driven thin film equation

Cited by 16 publications

References 27 publications

Numerical investigation of the generalized lubrication equation

Numerical investigation of the generalized lubrication equation

Numerical Comparison of Weno Type Schemes to the Simulations of Thin Films

Numerical studies of the fingering phenomena for the thin film equation

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