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fvmon

Nonlinear finite volumes schemes research group:

Publications

[1] 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

[2] 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. S1064562407050249.pdf

[3] 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

[4] 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

[5] 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

[6] 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

[7] 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

[8] 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

[9] 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.

[10] 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

[11] 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

[12] 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

[13] K.D.Nikitin, K.M.Terekhov, Y.V.Vassilevski. “A monotone nonlinear finite volume method for diffusion equations and multiphase flows” // Computational Geosciences, DOI: 10.1007/s10596-013-9387-6.nik-ter-vas-13.pdf

[14] 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

[15] 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

[16] 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

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

[18] 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

fvmon.txt · Last modified: 2018/08/16 16:40 by Kirill Nikitin