Research

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====== Kirill Dm. Nikitin ======

{{:ru:people:nikitin_cv_07_23.pdf | Curriculum Vitae}}

===== Contacts =====

  * e-mail: nikitin.kira (at) gmail.com
  * LinkedIn: [[http://linkedin.com/in/kirill-d-nikitin/|Kirill Nikitin]]

===== Member of =====

  * [[:freesurface|]]
  * [[:fvmon|]]

===== Publications =====

==== Free surface flows ====

[1] K. Nikitin, Y.Vassilevski, R.Yanbarisov, "An implicit scheme for simulation of free surface non-Newtonian fluid flows on dynamically adapted grids" %%//%% Russian Journal of Numerical Analysis and Mathematical Modelling, Vol. 36, I. 3, (June 2021), pp. 165-176. {{freesurface::rjnamm_nvy_2021.pdf|PDF}}

[2] K. Nikitin, K.Terekhov, Y.Vassilevski, "Two methods of surface tension treatment in free surface flow simulations" %%//%% Applied Mathematics Letters, Vol. 86, (December 2018), pp. 236-242. {{::1-s2.0-s089396591830226x-main.pdf|PDF}}

[3] K. Nikitin, M.Olshanskii, K.Terekhov, Y.Vassilevski, "A splitting method for free surface flows over partially submerged obstacles" %%//%% Russian Journal of Numerical Analysis and Mathematical Modelling, Vol. 33, No. 2, (2018), pp. 95-110. {{::semisubmerged.pdf|PDF}}

[4] K. Nikitin, M. Olshanskii, K. Terekhov, Y. Vassilevski, R. Yanbarisov. "An adaptive numerical method for free surface flows passing rigidly mounted obstacles" %%//%% Computers and Fluids, Vol. 148, (2017), pp. 56-69. {{::1-s2.0-s0045793017300518-main.pdf|PDF}}

[5] K. Nikitin, K. Terekhov, M. Olshanskii, Y. Vassilevski. "A semi-largangian method on dynamically adapted octree meshes" %%//%% Russian Journal of Numerical Analysis and Mathematical Modelling, Vol. 30, No. 6, (2015), pp. 363-380. {{::semilagrn.pdf|PDF}}

[6] 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 {{::cmam-2014-0025.pdf|PDF}}

[7] 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, Vol. 103, (2015). {{ ::preprint_no13-24.pdf |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|PDF}}

[9] 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|PDF}}

[10] K.D.Nikitin "Finite volume method for advection-diffusion equation and multiphase flows", Ph.D. thesis, 2010. {{:nikitin-thesis.pdf|PDF}} (in Russian)

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

[12] 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.

[13] [[freesurface/jcp|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|PDF}}

[14] 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. {{ :nikitin-vassilevski-08.pdf |PDF}}

[15] 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)

==== Nonlinear FV methods for advection-diffusion and multi-phase flows ====

[16] I.Berre, et al. Verification benchmarks for single-phase flow in three-dimensional fractured porous media. %%//%% Advances in Water Resourcesthis, 2021, 147, 103759.

[17] R.Yanbarisov, K.Nikitin. Projection-based monotone embedded discrete fracture method for flow and transport in porous media. %%//%% Journal of Computational and Applied Mathematics, 2021, 392, 113484.

[18] K.Nikitin, R.Yanbarisov. Monotone embedded discrete fractures method for flows in porous media. %%//%% Journal of Computational and Applied Mathematics, 2020, 365, 112353.

[19] V.Kramarenko, K.Nikitin, Y.Vassilevski. A finite volume scheme with improved well
modeling in subsurface flow simulation. %%//%% Computational Geosciences, 2017. DOI: 10.1007/s10596-017-9685-5.
 {{:cg-knv-v3.pdf|}}

[20] И.В.Капырин, К.Д.Никитин, А.В.Расторгуев, В.В.Сускин. Верификация моделей ненасыщенной фильтрации и переноса в зоне аэрации на примере расчетного кода GeRa %%//%% Вопросы атомной науки и техники, серия Математическое моделирование физических процессов, No. 1, (2017), С.60-75.

[21] K.Nikitin, K.Novikov, Y.Vassilevski. Nonlinear finite volume method with discrete maximum principle for the two-phase flow model %%//%% Lobachevskii Journal of Mathematics, Vol.37, No.5, (2016), 570–581. http://dx.doi.org/10.1134/S1995080216050097

[22] K.Nikitin, V.Kramarenko, Y. Vassilevski. Enhanced Nonlinear Finite Volume Scheme for Multiphase Flows %%//%% ECMOR-XV, 2016. http://www.earthdoc.org/publication/publicationdetails/?publication=86236

[23] V.Kramarenko, K.Nikitin, Y.Vassilevski. A nonlinear correction FV scheme for near-well regions. %%//%% Finite Volumes for Complex Applications VIII, 2017.

[24] I.Konshin, I.Kapyrin, K.Nikitin, K.Terekhov. Application of the parallel INMOST platform to subsurface flow and transport modelling %%//%% Parallel Processing and Applied Mathematics, Lecture Notes in Computer Science, Vol.9574, (2016), 277-286. http://dx.doi.org/10.1007/978-3-319-32152-3_26

[25] K.D.Nikitin, K.M.Terekhov, Y.V.Vassilevski, "Multiphase flows -- nonlinear monotone FV scheme and dynamic grids" %%//%% ECMOR XIV - 14th European conference on the mathematics of oil recovery, (2014).

[26] I.V.Kapyrin, K.D.Nikitin, K.M.Terekhov, Y.V.Vassilevski, "Nonlinear monotone FV schemes for radionuclide geomigration and multiphase flow models" %%//%% Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems. – Springer International Publishing, (2014), pp. 655-663.

[27] K.D.Nikitin, K.M.Terekhov, Y.V.Vassilevski, "A monotone nonlinear finite volume method for diffusion equations and multiphase flows" %%//%% Computational Geosciences: Vol. 18, No 3 (2014), pp 311-324, DOI: 10.1007/s10596-013-9387-6. {{:nik-ter-vas-13.pdf|}}

[28] K.D.Nikitin, Y.V.Vassilevski. "A monotone non-linear finite volume method for advection-diffusion equations and multiphase flows." %%//%% 13th European Conference on the Mathematics of Oil Recovery, (2012), pp.1-21. {{:nik-vas-ecmor2012.pdf|PDF}}

[29] K.Nikitin, A.Danilov, I.Kapyrin, Yu.Vassilevski. "Application of nonlinear monotone finite volume schemes to advection-diffusion problems." %%//%% Finite Volumes for Complex Applications VI – Problems & Perspectives, Vol.1, (2011), pp.761-769.

[30] K.D.Nikitin, Y.V.Vassilevski. "A monotone finite folume method for advection-diffusion equations on unstructured polyhedral meshes in 3D." %%//%% Russian Journal of Numerical Analysis and Mathematical Modelling, Vol.25, No.4, (2010), pp.335-358. {{:nikitin-vassilevski-10.pdf|PDF}}

[31] К.Д.Никитин. "Нелинейный метод конечных объемов для задач двухфазной фильтрации." %%//%% Математическое моделирование, Т.22, №11, (2010), С.131-147 {{:nikitin10.pdf|PDF}}\\
//K.D.Nikitin. "Nonlinear finite volume method for two-phase flows." %%//%% Mathematical Modelling, Vol.22, No.11, (2010), pp.131-147. (in Russian)//

----

=== The research was supported by ===
  * Russian Science Foundation grants 18-71-10111;
  * RFBR grants 12-01-31275, 12-01-33084, 14-01-00830, 15-35-20991 and 17-01-00886;
  * Federal program grants № P1127, P753, 02.740.11.0746, 14.740.11.1389 and 14.514.11.4057;
  * Russian President grant MK-7159.2013.1 and MK-2951.2017.1.

----
===== Visualization =====

=== 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.

[[http://dodo.inm.ras.ru/research/_media/movies:inviscid1.mp4|{{:movies:inviscid1.png?518x103|Adaptively refined grid}}]]

[[http://dodo.inm.ras.ru/research/_media/movies:inviscid2.mp4|{{:movies:inviscid2.png?518x103|Adaptively refined  grid}}]]

=== Metro Station ===

Flooding of the Polezhaevskaya Moscow Metro Station

[[http://dodo.inm.ras.ru/research/_media/movies:station:station-2.mp4|{{:movies:station:0071.png?270x180|Flooding of the Polezhaevskaya Moscow Metro Station}}]]


=== Sayano–Shushenskaya Dam ===

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

[[http://dodo.inm.ras.ru/research/_media/movies:bd:hes-break2.mp4|{{:movies:bd:hes-break2.png?270x180|Break of the Sayano–Shushenskaya Dam}}]]
[[http://dodo.inm.ras.ru/research/_media/movies:bd:hes-landslide2.mp4|{{:movies:bd:hes-landslide.png?270x180|Landslide over the Sayano–Shushenskaya Dam}}]]

=== 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

{{:movies:bd:bd_scheme_1.jpg?270x180|Breaking dam scheme}}
[[http://dodo.inm.ras.ru/research/_media/movies:bd:bd.mp4|{{:movies:bd:bd.png?270x180|Breaking dam}}]]

{{:movies:bd:dam-1.png?250|}}{{:movies:bd:front_new.png?240x210|}}

=== Flooding the city ===

[[http://dodo.inm.ras.ru/research/_media/movies:city:city1.mp4|{{:movies:city:city1.jpg?270x180|Flood}}]]
[[http://dodo.inm.ras.ru/research/_media/movies:city:city2.mp4|{{:movies:city:city2.jpg?270x180|Flood}}]]
[[http://dodo.inm.ras.ru/research/_media/movies:city:city3.mp4|{{:movies:city:city3-2.png?270x180|Flood}}]]
[[http://dodo.inm.ras.ru/research/_media/movies:city:city4.mp4|{{:movies:city:city4.png?380x180|Flood}}]]

=== A drop, falling into a shallow water ===

[[http://dodo.inm.ras.ru/research/_media/movies:drop:dropfall.mp4|{{:movies:drop:dropfall.png?270x180|Drop}}]]
[[http://dodo.inm.ras.ru/research/_media/movies:drop:falling_drops.mp4|{{:movies:drop:falling_drops.png?270x150|Drop}}]]

=== Boat under the waves ===

[[http://dodo.inm.ras.ru/research/_media/movies:bay:yalikbay3.mp4|{{:movies:bay:yalikbay3.jpg?270x180|Bay}}]]
[[http://dodo.inm.ras.ru/research/_media/movies:bay:yalikbay4.mp4|{{:movies:bay:yalikbay4.jpg?270x180|Bay}}]]

=== Model of Armadillo ===

[[http://dodo.inm.ras.ru/research/_media/movies:armadillo:arma1.mp4|{{:movies:armadillo:arma1.jpg?270x180|Armadillo}}]]
[[http://dodo.inm.ras.ru/research/_media/movies:armadillo:arma2.mp4|{{:movies:armadillo:arma2.jpg?270x180|Armadillo}}]]
[[http://dodo.inm.ras.ru/research/_media/movies:armadillo:arma3.mp4|{{:movies:armadillo:arma3.jpg?270x180|Armadillo}}]]
[[http://dodo.inm.ras.ru/research/_media/movies:armadillo:arma5.mp4|{{:movies:armadillo:arma5.jpg?270x180|Armadillo}}]]

=== Waves on a surface ===

[[http://dodo.inm.ras.ru/research/_media/movies:wave:wave1.mp4|{{:movies:wave:wave1.jpg?270x180|Filling a glass}}]]
[[http://dodo.inm.ras.ru/research/_media/movies:wave:wave2.mp4|{{:movies:wave:wave2.jpg?270x180|Filling a glass}}]]

=== Filling a glass with a liquid ===

[[http://dodo.inm.ras.ru/research/_media/movies:glass:glass3.mp4|{{:movies:glass:glass3.jpg?270x180|Filling a glass}}]]
[[http://dodo.inm.ras.ru/research/_media/movies:glass:glass8.mp4|{{:movies:glass:glass8.jpg?270x180|Filling a glass}}]]

=== A drop, falling into a glass with water ===

[[http://dodo.inm.ras.ru/research/_media/movies:drop:drop3-4.mp4|{{:movies:drop:drop3-4.jpg?270x180|Falling drop}}]]
[[http://dodo.inm.ras.ru/research/_media/movies:drop:drop3-5.mp4|{{:movies:drop:drop3-5.jpg?270x180|Falling drop}}]]
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