Geodesic
Mathematical modelling of wavy surface of liquid film falling down a vertical plane at moderate Reynolds' numbers
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 8 (2015) no. 4, pp. 30-39

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Development of periodic disturbances on free surface of water film falling down vertical plane for Reynolds' number $Re \in [5; 10]$ is investigated. The investigation is implemented in a scope of the nonlinear differential equation for evolution of free surface of falling down liquid film. The equation is solved by a finite differencies method at rectangular uniformly spaced grid. By researching the growth of unit inaccuracy, the conditions on parameters of computation grid for inaccuracies to be not increasing are obtained. As a result, waveforms of water film, time spent to form the regular wave mode and amplitudes of periodic disturbances are calculated. Calculated amplitudes and experimental ones are compared.
Keywords: liquid film; amplitude; waveform; nonlinear evolution of disturbances. 
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     author = {L. A. Prokudina and Ye. A. Salamatov},
     title = {Mathematical modelling of wavy surface of liquid film falling down a vertical plane at moderate {Reynolds'} numbers},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {30--39},
     publisher = {mathdoc},
     volume = {8},
     number = {4},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2015_8_4_a2/}
}
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L. A. Prokudina; Ye. A. Salamatov. Mathematical modelling of wavy surface of liquid film falling down a vertical plane at moderate Reynolds' numbers. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 8 (2015) no. 4, pp. 30-39. http://geodesic.mathdoc.fr/item/VYURU_2015_8_4_a2/