Mathematical modelling of wavy surface of liquid film falling down a vertical plane at moderate Reynolds' numbers

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.