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Free surface flows research group:


[1] K.D.Nikitin, Yu.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.

[2] K.D.Nikitin. “Computational technology for free surface flows with the use of dynamic hexahedral meshes.” // Computational Methods, Parallel Computing and Information Technology, MSU Publishing House, (2008), pp.183–193. (in Russian)

[3] 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

[4] 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” // Numerical geometry, grid generation and high perfomance computing, (2010), pp.25-32.

[5] K.D.Nikitin. “Realistic free surface flow modelling on adaptive octree meshes.” // SpbGU ITMO, Vol.70, No.6, (2010), pp.60-64. (in Russian)

[6] K.D.Nikitin “Finite volume method for advection-diffusion equation and multiphase flows”, Ph.D. thesis, 2010. nikitin-thesis.pdf (in Russian)

[7] K.D.Nikitin, M.A.Olshanskii, K.M.Terekhov, Yu.V.Vassilevski. “A numerical method for the simulation of free surface flows of viscoplastic fluid in 3D.” // Journal of Computational Mathematics, Vol.29, No.6, 2011, 605–622. notv2011.pdf

[8] K.D.Nikitin, M.A.Olshanskii, K.M.Terekhov, Yu.V.Vassilevski. “CFD technology for 3D simulation of large-scale hydrodynamic events and disasters.” // Russian Journal of Numerical Analysis and Mathematical Modelling, Vol.27, No.4, (2012), pp.399–412. notv2012.pdf

[9] M.A.Olshanskii, K.M.Terekhov, Yu.V.Vassilevski. “An octree-based solver for the incompressible Navier-Stokes equations with enhanced stability and low dissipation” // Computers and Fluids, (2013).

[10] A. Danilov, K. Nikitin, M. Olshanksii, K. Terekhov, Y. Vassilevski. “A unified approach for computing tsunami, waves, floods, and landslides” // Numerical mathematics and advanced applications – ENUMATH 2013 / Lecture Notes in Computational Science and Engineering, 2015, Vol. 103.

[11] K. Nikitin, M. Olshanskii, K. Terekhov, Y. Vassilevski. “A splitting method for numerical simulation of free surface flows of incompressible fluids with surface tension” // Computational Methods in Applied Mathematics, 2014, DOI:10.1515/cmam-2014-0025

The research is supported by

  • RFBR grants 11-01-00971-a, 12-01-00283-a, 12-01-91330-NNIO_a, 12-01-31275-mol_a and 14-01-00830;
  • Federal program grants № P753, 02.740.11.0746, 14.740.11.1389 and 14.514.11.4057.


Octree-MAC method

Simulation of the flow around cylinder with circular cross-section in inviscid limit with grid refined towards absolute value of vorticity. Colored in absolute value of vorticity.

Adaptively refined grid

Adaptively refined  grid

Metro Station

Flooding of the Polezhaevskaya Moscow Metro Station

Flooding of the Polezhaevskaya Moscow Metro Station

Sayano–Shushenskaya Dam

1) Break of the Sayano–Shushenskaya Dam, 2) Landslide over the Sayano–Shushenskaya Dam

Break of the Sayano–Shushenskaya Dam Landslide over the Sayano–Shushenskaya Dam

Viscoplastic dam break flow over incline plane [1]

Dam break flow over incline plane with alpha = 18°.
Herschel-Bulkley fluid with K = 47.68 Pa/s^n, n = 0.415, tau_s = 89 Pa.

Flow with no gate Flow with a gate

Freely oscillating viscoplastic droplet [1]

  • No plasticity: K = 1/150, tau_s = 0.
  • Low plasticity: K = 1/150, tau_s = 0.02.
  • High plasticity: K = 1/150, tau_s = 0.04.

No plasticity drop Low plasticity drop High plasticity drop

A von Karman vortex street behind cylinder

1) Semi-Lagrangian method (2nd order interpolation), 2) Semi-Lagrangian method (3srd order interpolation), 3) 2nd order upwind TVD

Semi-Lagrangian method Semi-Lagrangian method 2nd order upwind TVD

The breaking dam problem

1) The schematic apparatus from J. Martin, W. Moyce, Philos.Trans.R.Soc.Lond.Ser.A, V. 244 (1952), 2) animated numerical solution with the velocity field 3-4) comparison with the experimental data

Breaking dam scheme Breaking dam

Picnic chocolate


Flooding the city

Flood Flood Flood


A drop, falling into a shallow water

Drop Drop

Boat under the waves

Bay Bay

Model of Armadillo

Armadillo Armadillo Armadillo Armadillo

Waves on a surface

Filling a glass Filling a glass

Filling a glass with a liquid

Filling a glass Filling a glass

A drop, falling into a glass with water

Falling drop Falling drop

freesurface.1461161360.txt.gz · Last modified: 2016/04/20 14:09 by Kirill Nikitin