Research

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===== Nonlinear finite volumes schemes research group: =====
  * [[http://www.inm.ras.ru/persons/vuv.htm|Yuri Vassilevski]] (deputy director of [[http://www.inm.ras.ru/inm_en_ver/index.htm|INM RAS]], professor at [[http://www.msu.ru/|MSU]])
  * Ivan Kapyrin (Ph.D., senior researcher at [[http://www.inm.ras.ru/inm_en_ver/index.htm|INM RAS]])
  * [[http://dodo.inm.ras.ru/research/ru/people/nikitin|Kirill Nikitin]] (Ph.D., senior researcher at [[http://www.inm.ras.ru/inm_en_ver/index.htm|INM RAS]])
  * [[http://dodo.inm.ras.ru/research/ru/people/danilov|Alexander Danilov]] (Ph.D., senior researcher at [[http://www.inm.ras.ru/inm_en_ver/index.htm|INM RAS]])
  * Kirill Terekhov (Ph.D., researcher at [[http://www.inm.ras.ru/inm_en_ver/index.htm|INM RAS]], postdoc in [[http://www.stanford.edu/|Stanford University]])
  * [[http://dodo.inm.ras.ru/research/ru/people/chernyshenko|Alexey Chernyshenko]] (Ph.D., researcher at [[http://www.inm.ras.ru/inm_en_ver/index.htm|INM RAS]])
  * Ruslan Yanbarisov (Ph.D. student at [[http://www.inm.ras.ru/inm_en_ver/index.htm|INM RAS]])
===== Publications =====

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

[*] 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.

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

[*] 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|}}

[*] K.Nikitin, K.Novikov, Y.Vassilevski. Nonlinear finite volume method with discrete maximum principle for the two-phase flow model %%//%% Lobachevskii Journal of Mathematics, 2016, Vol.37, No.5, 570-581. 
 {{::lobachevskii_2016-v3.pdf|}}

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

[*] 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. {{:fvca7-kapniktervas.pdf|}}

[*] A.Chernyshenko, Y.Vassilevski. A Finite Volume Scheme with the Discrete Maximum Principle for Diffusion Equations on Polyhedral Meshes %%//%% Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects. – Springer International Publishing, 2014, pp.197-205. {{:chern-vass-fvca7.pdf|}}

[*] K.Terekhov, Y.Vassilevski. "Two-phase water flooding simulations on dynamic adaptive octree grids with two-point nonlinear fluxes. %%//%% Russian Journal of Numerical Analysis and Mathematical Modelling, Vol.28, No.3, (2013), pp.267-288. {{:terekhov-vassilevski-13.pdf|}}

[*] 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.3-4, (2013), 311-324, DOI: 10.1007/s10596-013-9387-6. {{:nik-ter-vas-13.pdf|}}

[*] K.Lipnikov, D.Svyatskiy, Y.Vassilevski. "Minimal stencil finite volume scheme with the discrete maximum principle." %%//%% Russian Journal of Numerical Analysis and Mathematical Modelling, Vol.27, No.4, (2012), 369-385. {{:lip-svy-vas-12.pdf|}}

[*] K.Nikitin, Y.Vassilevski. "A monotone finite volume method for advection diffusion equations and multiphase flows." %%//%% Proceedings ECMOR XIII, EAGE, (2012). {{:nik-vas-ecmor2012.pdf|}}

[*] 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, 761–769.

[*] K.Lipnikov, D.Svyatskiy, Y.Vassilevski. "A monotone finite volume method for advection-diffusion equations on unstructured polygonal meshes." %%//%% Journal of Computational Physics, Vol.229, (2010), pp.4017-4032. {{:lip-svy-vas-10.pdf|}}

[*] K.D.Nikitin, Y.V.Vassilevski. "A monotone finite volume 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|}}

[*] K.Nikitin. "Nonlinear finite volume method for two-phase flow in porous media." (in Russian) %%//%%
Mathematical Modelling, Vol.22, No.11, (2010), 131-147. {{:nikitin-10.pdf|}}

[*] K.Lipnikov, D.Svyatskiy, Y.Vassilevski. "Interpolation-free monotone finite volume method for diffusion equations on polygonal meshes." %%//%% Journal of Computational Physics, Vol.228, No.3, (2009), pp.703-716.{{:lip-svy-vas-09.pdf|}}

[*] A.A.Danilov, Y.V.Vassilevski. "A monotone nonlinear finite volume method for diffusion equations on conformal polyhedral meshes." %%//%% Russian Journal of Numerical Analysis and Mathematical Modelling, Vol.24, No.3, (2009), pp.207-227. {{:danilov-vassilevski-09.pdf|}}

[*] Y.Vassilevski, I.Kapyrin, "Two splitting schemes for nonstationary convection-diffusion problems on tetrahedral meshes." %%//%% Comp. Math. and Math. Phys. Vol.48, No.8, (2008), 1349-1366. {{:kap-vas-08.pdf.pdf|}}

[*] I.V.Kapyrin. "A Family of Monotone Methods for the Numerical Solution of Three-Dimensional Diffusion Problems on Unstructured Tetrahedral Meshes. %%//%% Doklady Mathematics, 2007, Vol. 76, No. 2, pp. 734–738. {{https://link.springer.com/content/pdf/10.1134/S1064562407050249.pdf}}

[*] K.Lipnikov, D.Svyatskiy, M.Shashkov, Y.Vassilevski. "Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes." %%//%% Journal of Computational Physics, Vol.227, (2007), pp.492-512. {{:lip-svy-shash-vas-07.pdf|}}
Research

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