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Kirill Dm. Nikitin

Contacts

  • e-mail: nikitin.kira (at) gmail.com

Member of

Publications

Free surface flows

[1] K.D.Nikitin, M.A.Olshanskii, K.M.Terekhov, Y.V.Vassilevski, R.M.Yanbarisov. «An adaptive numerical method for free surface flows passing rigidly mounted obstacles» // Computers and Fluids, Vol.148, (2017), pp.56-69. http://dx.doi.org/10.1016/j.compfluid.2017.02.007

[2] 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

[3] 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.

[4] 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

[5] K.D.Nikitin, M.A.Olshanskii, K.M.Terekhov, Yu.V.Vassilevski. «Numerical modelling of viscoplastic free surface flows in complex 3D geometries.» // Proc. of European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2012.

[6] 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

[7] К.Д.Никитин «Метод конечных объемов для задачи конвекции-диффузии и моделей двухфазных течений.» Кандидатская диссертация, 2010. nikitin-thesis.pdf
K.D.Nikitin «Finite volume method for advection-diffusion equation and multiphase flows», Ph.D. thesis, 2010. nikitin-thesis.pdf (in Russian)

[8] 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.
K.D.Nikitin. «Realistic free surface flow modelling on adaptive octree meshes.» // SpbGU ITMO, Vol.70, No.6, (2010), pp.60-64. (in Russian)

[9] 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.

[10] 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.

[11] 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.

[12] 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

Advection-diffusion problems and multi-phase flows

[13] 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.

[14] 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

[15] 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

[16] 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

[17] 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

[18] 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).

[19] 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.

[20] 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

[21] 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.

[22] 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

[23] К.Д.Никитин. «Нелинейный метод конечных объемов для задач двухфазной фильтрации.» // Математическое моделирование, Т.22, №11, (2010), С.131-147 nikitin10.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

  • 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.

Visualizations:

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

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

  • 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

Drop

Flooding the city

Flood 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

ru/people/nikitin.txt · Последние изменения: 2017/10/02 18:05 — Kirill Nikitin