THIN FILM FLOW ON AN INCLINED CHANNEL

Leo Hari Wiryanto (Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia)
Sudi Mungkasi (Department of Mathematics, Faculty of Science and Technology, Sanata Dharma University, Indonesia)
Ikha Magdalena (Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia)

BAREKENG: Jurnal Ilmu Matematika dan Terapan
Vol 20 No 3 (2026): BAREKENG: Journal of Mathematics and Its Application

A two-dimensional fluid is considered on an inclined channel. The depth of the fluid is small, so that it can be modeled as a single equation of the fluid depth, from the lubrication theory. The model is then solved numerically by an implicit finite difference method, to observe the surface wave propagation from the parameters such as the inclination of the channel and the ratio of the fluid thickness with respect to the wavelength. The effect of non-linearity of the model indicates that the wave propagates with changing the form, decreasing the amplitude, and tending to an almost shock wave. Those are simulated in this paper.