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[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. 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. 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. 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. 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. 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 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). 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. 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. PDF
[10] K.D.Nikitin «Finite volume method for advection-diffusion equation and multiphase flows», Ph.D. thesis, 2010. 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] 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. 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. 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)
[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. 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. PDF
[31] К.Д.Никитин. «Нелинейный метод конечных объемов для задач двухфазной фильтрации.» // Математическое моделирование, Т.22, №11, (2010), С.131-147 PDF
K.D.Nikitin. «Nonlinear finite volume method for two-phase flows.» // Mathematical Modelling, Vol.22, No.11, (2010), pp.131-147. (in Russian)
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.
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.
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