A corresponding member of the Russian Academy of Sciences, Professor Yuri Vassilevski is the Deputy Director of the Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences; the Head of the Department of Computational Technologies and Modelling in Geophysics and Biomathematics at Moscow Institute of Physics and Technology; the Head of the Laboratory of Mathematical Modelling in Medicine at Sechenov Univiersity, Professor at Lomonosov Moscow State University; Managing Editor of the Russian Journal of Numerical Analysis and Mathematical Modelling; Editor of the International Journal for Numerical Methods in Biomedical Engineering and the Journal on Computational Mathematics and Mathematical Physics, and a reviewer for over twenty scientific journals including the Journal of Computational Physics, Computer Methods in Applied Mechanics and Engineering, and the SIAM Journal on Scientific Computing. He was the PIin the Russian Science Foundation Project “Multiscale modeling of blood flow system in personalized medical technologies of cardiology, vascular neurology, oncology,” 2014–2018 (25 researchers), and in the ExxonMobil-INM Project “Parallel iterative solution of linear systems on multi-core clusters,” 2013–2017 (9 researchers). He is the author or co-author of over one hundred journal papers, three monographs, and two textbooks. His research interests include the theory of quasi-optimal meshes, mesh generation and adaptation, iterative methods for PDEs, discretization methods for PDEs, reservoir simulation, computational fluid dynamics, and computational hemodynamics.Dr. Kirill Terekhov is a Researcher at the Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, and former postdoctoral scholar at Stanford University. He was the main developer of the INMOST library, reservoir simulator, and free-surface flow solver. He is a reviewer for several scientific journals including Advances in Water Resources, Journal of Computational Physics, Computational Geosciences, etc. He is the author or co-author of over twenty papers and one monograph. His research interests include reservoir simulation, computational fluid dynamics, discretization schemes, multiphase flows, and free-surface flows.Dr. Kirill Nikitin is a Senior Researcher at the Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, and a reviewer for the Journal of Computational Physics, Journal of Computational Geosciences, and Russian Journal of Numerical Analysis and Mathematical Modelling. He is the PI in the Russian Science Foundation project “New numerical models and methods for solving the multi-physical problems of effective oil and gas recovery and safe disposal of radioactive waste” (2018-2021), and other completed projects based on Russian Foundation for Basic Research grants (2015–2016, 2012–2013), Russian President grants (2013–2014, 2017-2018), and Russian Ministry of Education and Science contract (2011–2013). He is the author or co-author of over twenty journal papers. His research interests include reservoir simulation, computational fluid dynamics, discretization schemes, multiphase flows, and free-surface flows.Dr. Ivan Kapyrin is a Senior Researcher at the Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences; Laboratory Head at the Nuclear Safety Institute of the Russian Academy of Sciences; and an Associate Professor at the Moscow Institute of Physics and Technology. He is the Leader of GeRa hydrogeological software development, a code designed for modelling groundwater flow and radionuclide transport in geological media (ca. 15 researchers involved). He is the co-author of the GEOPOLIS numerical model for the deep well radioactive waste injection site “Zheleznogorskii”. He is the author or co-author of over ten journal papers and one textbook. His research interests include groundwater flow and transport modelling, discretization methods for PDEs and site applications of hydrogeological models.

• Chapter 1 - Introduction.- Chapter 2 - Monotone finite volume method on general meshes.- Chapter 3 - Application of MFV in reservoir simulatio.- Chapter 4 - Application of FVM in modelling of subsurface radionuclide migration.- Chapter 5 - Application of MFV in modelling of coagulation of blood flow.- Chapter 6 - INMOST platform technologies for numerical model development.

A corresponding member of the Russian Academy of Sciences, Professor Yuri Vassilevski is the Deputy Director of the Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences; the Head of the Department of Computational Technologies and Modelling in Geophysics and Biomathematics at Moscow Institute of Physics and Technology; the Head of the Laboratory of Mathematical Modelling in Medicine at Sechenov Univiersity, Professor at Lomonosov Moscow State University; Managing Editor of the Russian Journal of Numerical Analysis and Mathematical Modelling; Editor of the International Journal for Numerical Methods in Biomedical Engineering and the Journal on Computational Mathematics and Mathematical Physics, and a reviewer for over twenty scientific journals including the Journal of Computational Physics, Computer Methods in Applied Mechanics and Engineering, and the SIAM Journal on Scientific Computing. He was the PIin the Russian Science Foundation Project “Multiscale modeling of blood flow system in personalized medical technologies of cardiology, vascular neurology, oncology,” 2014–2018 (25 researchers), and in the ExxonMobil-INM Project “Parallel iterative solution of linear systems on multi-core clusters,” 2013–2017 (9 researchers). He is the author or co-author of over one hundred journal papers, three monographs, and two textbooks. His research interests include the theory of quasi-optimal meshes, mesh generation and adaptation, iterative methods for PDEs, discretization methods for PDEs, reservoir simulation, computational fluid dynamics, and computational hemodynamics.Dr. Kirill Terekhov is a Researcher at the Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, and former postdoctoral scholar at Stanford University. He was the main developer of the INMOST library, reservoir simulator, and free-surface flow solver. He is a reviewer for several scientific journals including Advances in Water Resources, Journal of Computational Physics, Computational Geosciences, etc. He is the author or co-author of over twenty papers and one monograph. His research interests include reservoir simulation, computational fluid dynamics, discretization schemes, multiphase flows, and free-surface flows.Dr. Kirill Nikitin is a Senior Researcher at the Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, and a reviewer for the Journal of Computational Physics, Journal of Computational Geosciences, and Russian Journal of Numerical Analysis and Mathematical Modelling. He is the PI in the Russian Science Foundation project “New numerical models and methods for solving the multi-physical problems of effective oil and gas recovery and safe disposal of radioactive waste” (2018-2021), and other completed projects based on Russian Foundation for Basic Research grants (2015–2016, 2012–2013), Russian President grants (2013–2014, 2017-2018), and Russian Ministry of Education and Science contract (2011–2013). He is the author or co-author of over twenty journal papers. His research interests include reservoir simulation, computational fluid dynamics, discretization schemes, multiphase flows, and free-surface flows.Dr. Ivan Kapyrin is a Senior Researcher at the Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences; Laboratory Head at the Nuclear Safety Institute of the Russian Academy of Sciences; and an Associate Professor at the Moscow Institute of Physics and Technology. He is the Leader of GeRa hydrogeological software development, a code designed for modelling groundwater flow and radionuclide transport in geological media (ca. 15 researchers involved). He is the co-author of the GEOPOLIS numerical model for the deep well radioactive waste injection site “Zheleznogorskii”. He is the author or co-author of over ten journal papers and one textbook. His research interests include groundwater flow and transport modelling, discretization methods for PDEs and site applications of hydrogeological models.

• Chapter 1 - Introduction.- Chapter 2 - Monotone finite volume method on general meshes.- Chapter 3 - Application of MFV in reservoir simulatio.- Chapter 4 - Application of FVM in modelling of subsurface radionuclide migration.- Chapter 5 - Application of MFV in modelling of coagulation of blood flow.- Chapter 6 - INMOST platform technologies for numerical model development.