Kirill Dm.
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You can playback or download few animated free-surface incompressible fluid flows. (Click a picture to run a movie) All flows are numerical solutions to the Navier-Stokes equations coupled with level-set function equation. The method and solver are given in:

[1] К.Д.Никитин. "Технология расчёта течений со свободной границей с использованием динамических гексаэдральных сеток." \\ Численные методы, параллельные вычисления и информационные технологии: Сборник научных трудов / Под ред. Вл.В.Воеводина и Е.Е.Тыртышникова, Изд-во МГУ, (2008), с.183-198.

[2] K.D.Nikitin, Y.V.Vassilevski. "Free surface flow modelling on dynamically refined hexahedral meshes." \\ Russian Journal of Numerical Analysis and Mathematical Modelling, Vol.23, No.5, (2008), pp.469-485.

[3] К.Д.Никитин, А.Ф.Сулейманов, К.М.Терехов. "Технология моделирования течений со свободной поверхностью в реалистичных сценах." \\ Труды математического общества им. Н.И.Лобачевского, Казань: Казан.матем.об-во, T.39, (2009), с.305-307.

[6] К.Д.Никитин. "Реалистичное моделирование свободной водной поверхности на адаптивных сетках типа восьмеричное дерево." \\ Научно-технический вестник СПбГУ ИТМО, Т.70, №6, (2010), С.60-64.

[7] K.D.Nikitin, M.A.Olshanskii, K.M.Terekhov, Y.V.Vassilevski. "Preserving distance property of level set function and simulation of free surface flows on adaptive grids" // Численная геометрия, построение расчетных сеток и высокопроизводительные вычисления, (2010), pp.25-32.

[8] K. D. Nikitin, M.A. Olshanskii, K. M. Terekhov, Yu. V. Vassilevski, Numerical simulations of free surface flows on adaptive cartesian grids with level set function method, // submitted, November 2010.

A drop, falling into a glass with water. (2008)

Filling a glass with a liquid. (2008)

Waves on a surface. (2008)

"Fluidized" model. (2009)

Flooding the city. (2009)

Boat under the waves. (2010)

Breaking dam problem. (2010)
See [8] for comparative analysis of numerical results and experimental data from J. Martin, W. Moyce, // Philos.Trans.R.Soc.Lond.Ser.A, V.244 (1952).

The Zalesak's disk test - animation of a rotated slotted cylinder. (2010)
Octree grid gradely refined from h1 in air and h2 in water to h3 near free surface.
mesh \ particles no particles with particles
h1 = 1/64
h2 = 1/64
h3 = 1/64
h1 = 1/16
h2 = 1/32
h3 = 1/128
h1 = 1/16
h2 = 1/32
h3 = 1/256
h1 = 1/16
h2 = 1/32
h3 = 1/512

The oscillating droplet problem (2010)
(see linear analysis in H. Lamb, Hydrodynamics, Cambridge University Press, 1932): At initial moment the fluid is in rest, but the mean curvature of the surface is not constant, and an unbalanced surface tension force causes droplet oscillation. The fluid motion is solely driven by the surface tension forces.

Droplet falling in a shallow water pool: Numerical solution vs. nature phenomena.

© 2010 Nikitin Kirill