You can playback or download few animated free-surface incompressible fluid flows. All flows are numerical solutions to the Navier-Stokes equations coupled with level-set function equation. The method and solver are given in 

[1] 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, {{:notv9.pdf|}}

Animated solutions from the paper [1] (Click a picture to run a movie): 
  * The Zalesak's disk test (animation of a rotated slotted cylinder): 1) Uniform grid with h=1/64, 2) Octree grid gradely refined from h=1/16 to h=1/256, 3) Octree grid gradely refined from h=1/16 to h=1/512, and 4) Octree grid gradely refined from h=1/16 to h=1/256 with particle method 

[[http://www.inm.ras.ru/research/_media/movies:zalesak:64_64_64.avi|{{:movies:zalesak:64_64_64.png?270x180|Zalesak's disk}}]]
[[http://www.inm.ras.ru/research/_media/movies:zalesak:256_32_16.avi|{{:movies:zalesak:256_32_16.png?270x180|Zalesak's disk}}]]
[[http://www.inm.ras.ru/research/_media/movies:zalesak:512_32_16.avi|{{:movies:zalesak:512_32_16.png?270x180|Zalesak's disk}}]]
[[http://www.inm.ras.ru/research/_media/movies:zalesak:256_32_16_particles.avi|{{:movies:zalesak:256_32_16_particles.png?270x180|Zalesak's disk}}]]

  * The breaking dam problem (also known as collapsing water column): The schematic apparatus from J. Martin, W. Moyce, Philos.Trans.R.Soc.Lond.Ser.A, V. 244 (1952) and animated numerical solutions 1) velocity field 2) without particles method 3) with particles 

{{:movies:bd:bd_scheme_1.jpg?270x180|Breaking dam scheme}}
[[http://www.inm.ras.ru/research/_media/movies:bd:bd.avi|{{:movies:bd:bd.png?270x180|Breaking dam}}]]
[[http://www.inm.ras.ru/research/_media/movies:bd:bd1.avi|{{:movies:bd:bd.jpg?270x180|Breaking dam}}]]
[[http://www.inm.ras.ru/research/_media/movies:bd:bd2.avi|{{:movies:bd:bd.jpg?270x180|Breaking dam}}]]

See [1] for comparative analysis of numerical and experimental data. 
  * The oscillating droplet problem (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. 

[[http://www.inm.ras.ru/research/_media/movies:drop:osc_drop.avi|{{:movies:drop:osc_drop.png?270x180|Oscillating droplet}}]]

See [1] for the discussion of the physical relevance of the numerical solutions. 


[[|More free surface flows animations]]


Contributers:
  * [[http://dodo.inm.ras.ru/nikitink/portfolio.html|Kirill Nikitin]] (PhD student at [[http://www.inm.ras.ru/inm_en_ver/index.htm|INM RAS]])
  * [[http://www.mathcs.emory.edu/~molshan|Maxim Olshanskii]] (professor at [[http://www.msu.ru/|MSU]])
  * Artem Suleimanov (student at [[http://www.msu.ru/|MSU]])
  * Kirill Terekhov (PhD student at [[http://www.inm.ras.ru/inm_en_ver/index.htm|INM RAS]])
  * Yuri Vassilevski (professor at [[http://www.inm.ras.ru/inm_en_ver/index.htm|INM RAS]])