51) S. Waziri, G. Ren, P. Tomin, B. Guyaguler. Nonlinear Acceleration of the Iterative-Sequentially Coupled Flow and Geomechanics Fixed Stress Scheme. Rock Mechanics and Rock Engineering, 2025.* springer.com
50) R. Hasanzade, P. Tomin, H. Tchelepi. Adaptive Conservative Explicit/Implicit Method that Overcomes the Global Limit on the Timestep Size. SPE-223925-MS, SPE Reservoir Simulation Conference, Galveston, Texas, USA, March 2025. onepetro.org
49) G. Ren, P. Tomin, B. Guyaguler, X. Wen. Numerical Investigation of the Poroelasticity Impact on Hydraulic Fracturing. SPE-223905-MS, SPE Reservoir Simulation Conference, Galveston, Texas, USA, March 2025. onepetro.org
48) V. Magri, N. Castelletto, D. Osei-Kuffuor, R. Settgast, M. Cusini, W. Tobin, R. Aronson, P. Tomin. A Multigrid Reduction Framework for Efficient and Scalable Multiphysics Simulations. SPE-223898-MS, SPE Reservoir Simulation Conference, Galveston, Texas, USA, March 2025. onepetro.org
47) J. An, S. Waziri, G. Ren, P. Tomin, Y. Li, K. Zaki. Study on Coupling Parameters for Flow-Geomechanics Simulation Schemes. SPE-223890-MS, SPE Reservoir Simulation Conference, Galveston, Texas, USA, March 2025. onepetro.org
46) R. Aronson, P. Tomin, N. Castelletto, F. Hamon, J. White, H. Tchelepi. Pressure stability in explicitly coupled simulations of poromechanics with application to CO2 sequestration. Computer Methods in Applied Mechanics and Engineering, V. 435, doi:10.1016/j.cma.2024.117633, 2024.* sciencedirect.com text
45) R. Settgast, R. Aronson, J. Besset, A. Borio, Q. Bui, T. Byer, N. Castelletto, A. Citrain, B. Corbett, J. Corbett, P. Cordier, M. Cremon, C. Crook, M. Cusini, F. Fei, S. Frambati, J. Franc, A. Franceschini, M. Frigo, P. Fu, T. Gazzola, H. Gross, F. Hamon, B. Han, Y. Hao, R. Hasanzade, M. Homel, J. Huang, T. Jin, I. Ju, D. Kachuma, M. Karimi-Fard, T. Kim, S. Klevtsov, A. Lapene, A. Mazuyer, M. N'diaye, D. Osei-Kuffuor, S. Povolny, G. Ren, S. Semnani, C. Sherman, M. Rey, H. Tchelepi, W. Tobin, P. Tomin, L. Untereiner, A. Vargas, S. Waziri, X. Wen, J. White, H. Wu. GEOS: A performance portable multi-physics simulation framework for subsurface applications. Journal of Open Source Software, V. 9 (102), doi:10.21105/joss.06973, 2024.* text
44) H. Gross, R. Settgast, R. Aronson, A. Borio, Q. Bui, N. Castelletto, B. Corbett, P. Cordier, M. Cremon, M. Cusini, S. Frambati, J. Franc, T. Gazzola, F. Hamon, J. Huang, D. Kachuma, M. Karimi-Fard, S. Klevtsov, A. Lapene, V. Magri, A. Mazuyer, M. N’diaye, D. Osei-Kuffuor, C. Sherman, H. Tchelepi, W. Tobin, P. Tomin, X. Wen, J. White. GEOS: Exascale, Multiphysics, Open-Source Simulation for CCS. 19th European Conference on the Mathematics of Geological Reservoirs, doi:10.3997/2214-4609.202437054, 2024. earthdoc.org
43) S. Waziri, G. Ren, P. Tomin, B. Guyaguler. Nonlinear acceleration of the iterative-sequentially coupled flow and geomechanics fixed stress scheme. 58th U.S. Rock Mechanics/Geomechanics Symposium, Golden, Colorado, USA, doi:10.56952/ARMA-2024-0501, 2024. onepetro.org
42) S. Lee, P. Tomin, Y. Efendiev. Convergent sequential fully implicit method for reservoir simulation. Journal of Computational Physics, doi:10.1016/j.jcp.2023.112442, 2023.* sciencedirect.com
41) J. Jiang, P. Tomin, H. Tchelepi. Accelerated Nonlinear Domain Decomposition Solver for Multi-phase Flow and Transport in Porous Media. Journal of Computational Physics, doi:10.1016/j.jcp.2023.112328, 2023.* sciencedirect.com
40) S. Watanabe, J. Natvig, P. Tomin. Strongly Coupled Prolongation in Multiscale Pressure Solver for High-Contrast Heterogeneous Reservoir Simulation. SPE-212231-MS, SPE Reservoir Simulation Conference, March 2023. onepetro.org
39) J. Natvig, D. Dias, F. Bratvedt, S. Watanabe, Z. Li, A. Kozlova, P. Tomin, J. Jiang, X. Shi. Multiscale Reservoir Simulation of High-Resolution Models. SPE-212231-MS, SPE Reservoir Simulation Conference, March 2023. onepetro.org
38) J. Li, P. Tomin, H. Tchelepi. Sequential fully implicit Newton method for flow and transport with natural black-oil formulation. Computational Geosciences, 2021.* springer.com text
37) Y. Zhou, J. Jiang, P. Tomin. Inexact Methods for Black-Oil Sequential Fully Implicit SFI Scheme. SPE-203900-MS, SPE Reservoir Simulation Conference, October 2021. onepetro.org
36) J. Li, P. Tomin, H. Tchelepi. Sequential fully implicit Newton method for compositional flow and transport. Journal of Computational Physics, 2021.* sciencedirect.com text
35) J. Jiang, P. Tomin, Y. Zhou. Inexact methods for sequential fully implicit (SFI) reservoir simulation. Computational Geosciences, 2021.* springer.com text
34) O. Fuks, F. Ibrahima, P. Tomin, H. A. Tchelepi. Uncertainty Propagation for Compositional Flow Using a Probability Distribution Method. Transport in Porous Media, V. 132, P. 113–133, 2020.* springer.com text
33) J. Li, Z. Y. Wong, P. Tomin, H. Tchelepi. Sequential implicit Newton method for coupled multi-segment wells. SPE-193833-MS, SPE Reservoir Simulation Conference, Galveston, Texas, USA, 10-11 April 2019. onepetro.org text
32) S. Gries, B. Metsch, K. Terekhov, P. Tomin. System-AMG for fully coupled reservoir simulation with geomechanics. SPE-193887-MS, SPE Reservoir Simulation Conference, Galveston, Texas, USA, 10-11 April 2019. onepetro.org text
31) O. Fuks, F. Ibrahima, P. Tomin, H. A. Tchelepi. Analysis of Travel Time Distributions for Uncertainty Propagation in Channelized Porous Systems. Transport in Porous Media, SI: Uncertainty Quantification and Multiple Scale Methods, V. 126(1), P. 115–137, 2019.* springer.com text
30) P. Tomin, D. Voskov. Robust And Accurate Formulation For Modeling Of Acid Stimulation. Proceedings of the 16th European Conference on the Mathematics of Oil Recovery, Barcelona, Spain, 3-6 September, 2018. earthdoc.org text
29) T. T. Garipov, P. Tomin, R. Rin. D. V. Voskov, H. A. Tchelepi. Unified thermo-compositional-mechanical framework for reservoir simulation. Computational Geosciences, V. 22(4), P. 1039–1057, 2018.* springer.com text
28) R. Shaik, P. Tomin, D. Voskov. Modelling of near-well acidization. 43rd Workshop on Geothermal Reservoir Engineering, Stanford University, Stanford, California, February 12-14, 2018. text presentation
27) R. Rin, P. Tomin, T. Garipov, D. Voskov, H. Tchelepi. General Implicit Coupling Framework for Multi-Physics Problems. SPE-182714-MS, SPE Reservoir Simulation Conference, Montgomery, Texas, USA, 20-22 February 2017. onepetro.org text
26) P. Tomin, I. Lunati. Investigating Darcy-scale assumptions by means of a multiphysics algorithm. Advances in Water Resources, SI: Pore scale modeling and experiments, V. 95, P. 80–91, 2016.* sciencedirect.com text
Multiphysics algorithms allow us to examine the assumptions of Darcy-scale models
Scale ratio based on pore geometry is justified only for linear single-phase flow
Dynamic spatial scales emerge in multiphase phenomena and weaken scale separation
Macro-parameters depend on the fluid distribution resulting from pore-scale physics
Macroscopic constitutive relationships depend on the specific flow regime
25) P. Tomin, I. Lunati. Spatiotemporal adaptive multiphysics simulations of drainage-imbibition cycles. Computational Geosciences, V. 20(3), P. 541–554, 2016.* springer.com text
24) P. Tomin, I. Lunati. Local-global splitting for spatiotemporal-adaptive multiscale methods. Journal of Computational Physics, V. 280, P. 214–231, 2015.* sciencedirect.com text
Local-global splitting as a framework for multiscale multiphysics simulations
Spatiotemporal adaptivity for the Multiscale Finite Volume method
Adaptive criteria based on the changes of coarse-scale quantities
Self-correcting scheme to improve the quality of multiscale approximation
Multiscale multiphysics simulations of two-phase flow in porous media
23) P. Tomin, I. Lunati. Spatiotemporal adaptive multiscale multiphysics simulations of two-phase flow. Proceedings of the 14th European Conference on the Mathematics of Oil Recovery, Catania, Sicily, Italy, 8–11 September 2014. earthdoc.org text
22) R. Künze, P. Tomin, I. Lunati. Local modeling of instability onset for global finger evolution. Advances in Water Resources, V. 70, P. 148–159, 2014.* sciencedirect.com text
Accurate modeling of instabilities requires resolving the critical wavelength
An adaptive multiscale algorithm is used to accurately model the instability onset
Large-scale and later-time accuracy is greatly improved
The adaptive algorithm is flexible and effective to describe finger statistics
If required, some regions can be refined during the entire simulation
21) D. Mitrushkin, P. Tomin. Simulation of flow in vuggy porous media. Actual Problems of Oil and Gas, V. 9, N. 1, 2014 (in Russian). oilgasjournal.ru
20) P. Tomin, I. Lunati. Hybrid Multiscale Finite Volume Method for Two-Phase Flow in Porous Media. Journal of Computational Physics, V. 250, P. 293–307, 2013.* sciencedirect.com text
19) P. Tomin, A. Pergament. Single Porosity Model for Fractured Formations. Proceedings of the 13th European Conference on the Mathematics of Oil Recovery, Biarritz, France, 10–13 September 2012. earthdoc.org text
18) P. Tomin, I. Lunati, A. Ferrari, R. Kuenze. A Framework for Hybrid Simulations of Two-phase Flow in Porous Media. Proceedings of the 13th European Conference on the Mathematics of Oil Recovery, Biarritz, France, 10–13 September 2012. earthdoc.org text
17) A. Pergament, P. Tomin. The study of relative phase-permeability functions for anisotropic media. Mathematical Models and Computer Simulations, V. 4, N. 1, P. 1–9, 2012.* springer.com mathnet.ru text
16) P. Tomin. Mathematical Modeling of Multiphase Flow in Fractured Media. Ph.D. thesis in Applied Mathematics and Computational Physics, 2011 (in Russian). synopsis text
15) A. Pergament, V. Semiletov, P. Tomin. On some multiscale algorithms for sector modeling in multiphase flow in porous media. Mathematical Models and Computer Simulations, V. 3, N. 3, P. 365–374, 2011.* springer.com mathnet.ru text
14) S. Akhmedsafin, S. Kirsanov, A. Laperdin, A. Krasovskiy, A. Balashov, D. Mitrushkin, P. Tomin. Search for the Best Solution for Choosing the Location of Planned Wells in the Gas Deposit Area. Bulletin of the CDC Rosnedra, N. 2, P. 35–42, 2011 (in Russian).* elibrary.ru text
13) P. Tomin. Application of Multiscale Algorithms for Solving Problems of Multiphase Flow in Anisotropic Media. Keldysh Institute Preprint, N. 14, 2011 (in Russian). keldysh.ru mathnet.ru
12) P. Tomin. On the Representative Elementary Volume Concept. Keldysh Institute Preprint, N. 13, 2011 (in Russian). keldysh.ru mathnet.ru
11) A. Pergament, V. Semiletov, P. Tomin. Multiscale Method for Numerical Simulation of Multiphase Flows in Giant Production Fields. Proceedings of the 12th European Conference on the Mathematics of Oil Recovery, Oxford, England, 6–9 September 2010. earthdoc.org text
10) A. Pergament, V. Semiletov, P. Tomin. Up- and Down-Scaling in Filtration Problem with Anisotropic Coefficients. Bulletin of the CDC Rosnedra, N. 4, P. 23–30, 2010 (in Russian).* oilvestnik.ru elibrary.ru text
9) P. Tomin. On Some Tracers Application to the Inter-Well Media Features Studying. Keldysh Institute Preprint, N. 86, 2010 (in Russian). keldysh.ru mathnet.ru
8) M. Zaslavsky, P. Tomin. On Modeling of Multiphase Flows in Fractured Media with Application to History Matching Problem. Keldysh Institute Preprint, N. 45, 2010 (in Russian). keldysh.ru mathnet.ru
7) D. Maksimov, N. Marchenko, V. Semiletov, P. Tomin. Some Nonlinear Convergence Improving Approaches in Numerical Simulation of Multiphase Flow Problems. Keldysh Institute Preprint, N. 44, 2010 (in Russian). keldysh.ru mathnet.ru
6) A. Pergament, V. Semiletov, P. Tomin. Multiscale Asynchronous Algorithms Based on the Superelement Method for Multiphase Flow. Proceedings of the 11th European Conference on the Mathematics of Oil Recovery, Bergen, Norway, 8–11 September 2008. earthdoc.org text
5) A. Pergament, V. Semiletov, P. Tomin. Mathematical Modeling of Multiphase Flow in Fractured Media. Proceedings of the 11th European Conference on the Mathematics of Oil Recovery, Bergen, Norway, 8–11 September 2008. earthdoc.org text
4) N. Marchenko, A. Pergament, S. Popov, V. Semiletov, P. Tomin. Hierarchy of Explicit-Implicit Difference Schemes for Multiphase Filtration Problems. Keldysh Institute Preprint, N. 97, 2008 (in Russian). keldysh.ru mathnet.ru
3) D. Maksimov, A. Tikhonov, P. Tomin. Parallel Computation Application for Reservoir Simulation. Bulletin of the CDC Rosnedra, N. 2, P. 69–78, 2007 (in Russian).* text
2) P. Tomin. Multiscale Algorithms Based on Finite Super Element Method for Two-Phase Flow Simulations. Keldysh Institute Preprint, N. 45, 2007 (in Russian). keldysh.ru mathnet.ru
1) P. Tomin. Inverse Problem of Measuring the Ultrashort Laser Pulse Parameters. Keldysh Institute Preprint, N. 51, 2006 (in Russian). keldysh.ru mathnet.ru
* – peer-reviewed