We present a robust and accurate numerical method for simulating gravity-driven, thin-film flow problems. The convection term in the governing equation is treated by a semi-implicit, essentially non-oscillatory scheme. The resulting nonlinear discrete equation is solved using a nonlinear full approximation storage multigrid algorithm with adaptive mesh refinement techniques. A set of representative numerical experiments are presented. We show that the use of adaptive mesh refinement reduces computational time and memory compared to the equivalent uniform mesh results. Our simulation results are consistent with previous experimental observations.
Bibliographical noteFunding Information:
Acknowledgements The corresponding author (J.S. Kim) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2011-0023794). The authors greatly appreciate the reviewers for their constructive comments and suggestions, which have improved the quality of this paper.
- Adaptive mesh refinement
- Nonlinear diffusion equations
- Nonlinear multigrid method
- Thin film
ASJC Scopus subject areas
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering