Model for multiphase fluid flows with interphase interaction taken into account
V. A. Balashov, E. B. Savenkov

This publication is cited in the following articles:

1. A. A. Zlotnik, T. A. Lomonosov, “Primenenie regulyarizovannykh uravnenii dinamiki geterogennykh binarnykh smesei dlya modelirovaniya fazovykh perekhodov voda-par”, Matem. modelirovanie, 37:1 (2025), 151–170    
2. A. A. Zlotnik, T. A. Lomonosov, “Application of Regularized Equations for Dynamics of Heterogeneous Binary Mixtures for Modeling Water–Vapor Phase Transitions”, Math Models Comput Simul, 17:3 (2025), 352  
3. Vladislav Balashov, Evgeny Savenkov, Aleksey Khlyupin, Kirill M. Gerke, “Two-phase regularized phase-field density gradient Navier–Stokes based flow model: Tuning for microfluidic and digital core applications”, Journal of Computational Physics, 2024, 113554  
4. A. S. Fedchenko, “Properties of Regularized Equations for Barotropic Gas Mixtures”, J Math Sci, 270:6 (2023), 815  
5. A. Zlotnik, T. Lomonosov, “On a doubly reduced model for dynamics of heterogeneous mixtures of stiffened gases, its regularizations and their implementations”, Chaos: An Interdisciplinary Journal of Nonlinear Science, 33:11 (2023)  
6. Chao Zhang, Lifeng Wang, “Thermorelaxing multicomponent flows investigated with a Baer-Nunziato-type model”, Phys. Rev. E, 108:4 (2023)  
7. Alexander Zlotnik, Timofey Lomonosov, “On Regularized Systems of Equations for Gas Mixture Dynamics with New Regularizing Velocities and Diffusion Fluxes”, Entropy, 25:1 (2023), 158  
8. V. A. Balashov, E. B. Savenkov, B. N. Chetverushkin, ““Digital Core” Technology and Supercomputer Computing”, Her. Russ. Acad. Sci., 93:1 (2023), 18  
9. A. A. Zlotnik, “On the construction of regularized equations of motion for a mixture of viscous incompressible fluids”, Dokl. Math., 106:2 (2022), 380–385          
10. Chao Zhang, Igor Menshov, Lifeng Wang, Zhijun Shen, “Diffuse interface relaxation model for two-phase compressible flows with diffusion processes”, Journal of Computational Physics, 466 (2022), 111356  
11. Alexander Zlotnik, Anna Fedchenko, Timofey Lomonosov, “Entropy Correct Spatial Discretizations for 1D Regularized Systems of Equations for Gas Mixture Dynamics”, Symmetry, 14:10 (2022), 2171  
12. Alexander Zlotnik, Anna Fedchenko, “On properties of aggregated regularized systems of equations for a homogeneous multicomponent gas mixture”, Math Methods in App Sciences, 45:15 (2022), 8906  
13. A. A. Zlotnik, A. S. Fedchenko, “On the Properties of a Quasihydrodynamic System of Equations for a Homogeneous Gas Mixture with a Common Regularizing Velocity”, Diff Equat, 58:3 (2022), 341  
14. Elizaveta Zipunova, Evgeny Savenkov, “Phase field model for electrically induced damage using microforce theory”, Mathematics and Mechanics of Solids, 27:6 (2022), 1111  
15. A. V. Ivanov, M. V. Kraposhin, T. G. Elizarova, “O novom metode regulyarizatsii uravnenii dvukhfaznoi neszhimaemoi sredy”, Preprinty IPM im. M. V. Keldysha, 2021, 061, 27 pp.    
16. A. A. Zlotnik, A. S. Fedchenko, “Svoistva agregirovannoi kvazigidrodinamicheskoi sistemy uravnenii gomogennoi gazovoi smesi s obschei regulyarizuyuschei skorostyu”, Preprinty IPM im. M. V. Keldysha, 2021, 077, 26 pp.    
17. V. A. Balashov, E. B. Savenkov, “Regulyarizovannaya model tipa fazovogo polya dlya opisaniya sistemy «zhidkost–tverdoe telo» s uchetom khimicheskikh reaktsii”, Preprinty IPM im. M. V. Keldysha, 2021, 082, 20 pp.    
18. Vladislav Balashov, Alexander Zlotnik, “On a New Spatial Discretization for a Regularized 3D Compressible Isothermal Navier–Stokes–Cahn–Hilliard System of Equations with Boundary Conditions”, J Sci Comput, 86:3 (2021)  
19. T. G. Elizarova, E. V. Shilnikov, “Numerical simulation of gas mixtures based on the quasi-gasdynamic approach as applied to the interaction of a shock wave with a gas bubble”, Comput. Math. Math. Phys., 61:1 (2021), 118–128            
20. Vladislav Balashov, “A regularized isothermal phase-field model of two-phase solid–fluid mixture and its spatial dissipative discretization equations”, Russian Journal of Numerical Analysis and Mathematical Modelling, 36:4 (2021), 197  
21. V.A. Balashov, “Dissipative spatial discretization of a phase field model of multiphase multicomponent isothermal fluid flow”, Computers & Mathematics with Applications, 90 (2021), 112  
22. V. A. Balashov, E. B. Savenkov, “Regulyarizovannaya model tipa fazovogo polya dlya opisaniya dinamiki sistemy «zhidkost-tverdoe telo»”, Preprinty IPM im. M. V. Keldysha, 2020, 096, 29 pp.    
23. I. S. Menshov, Ch. Zhang, “Interface capturing method based on the Cahn–Hilliard equation for two-phase flows”, Comput. Math. Math. Phys., 60:3 (2020), 472–483            
24. Balashov Vladislav, Savenkov Evgeny, “Direct fluid flow simulation at pore scale with regularized hydrodynamic equations”, J. Phys.: Conf. Ser., 1640:1 (2020), 012008  
25. V.A. Balashov, E.B. Savenkov, “Thermodynamically consistent spatial discretization of the one-dimensional regularized system of the Navier–Stokes–Cahn–Hilliard equations”, Journal of Computational and Applied Mathematics, 372 (2020), 112743  
26. Vladislav Balashov, Alexander Zlotnik, “AN ENERGY DISSIPATIVE SPATIAL DISCRETIZATION FOR THE REGULARIZED COMPRESSIBLE NAVIER-STOKES-CAHN-HILLIARD SYSTEM OF EQUATIONS”, Mathematical Modelling and Analysis, 25:1 (2020), 110  
27. Vladislav Balashov, Alexander Zlotnik, “An energy dissipative semi-discrete finite-difference method on staggered meshes for the 3D compressible isothermal Navier–Stokes–Cahn–Hilliard equations”, JCD, 7:2 (2020), 291  
28. T. G. Elizarova, A. A. Zlotnik, E. V. Shilnikov, “Regularized equations for numerical simulation of flows of homogeneous binary mixtures of viscous compressible gases”, Comput. Math. Math. Phys., 59:11 (2019), 1832–1847          
29. Kirill M. Gerke, Anna V. Isaeva, Marina V. Karsanina, Elena V. Shaporenko, Dmitry V. Korost, SPE Russian Petroleum Technology Conference, 2019  
30. V. A. Balashov, E. B. Savenkov, B. N. Chetverushkin, “DiMP-Hydro solver for direct numerical simulation of fluid microflows within pore space of core samples”, Math. Models Comput. Simul., 12:2 (2020), 110–124        
31. Kirill M. Gerke, Anna V. Isaeva, Marina V. Karsanina, Elena V. Shaporenko, Dmitry V. Korost, Day 3 Thu, October 24, 2019, 2019  
32. Vladislav Balashov, E. B. Savenkov, Springer Proceedings in Earth and Environmental Sciences, Physical and Mathematical Modeling of Earth and Environment Processes (2018), 2019, 374  
33. V. A. Balashov, E. B. Savenkov, “Chislennyi raschet dvumernykh techenii dvukhfaznoi zhidkosti s uchetom smachivaemosti s pomoschyu kvazigidrodinamicheskikh uravnenii”, Preprinty IPM im. M. V. Keldysha, 2018, 131, 18 pp.      
34. B. N. Chetverushkin, “Problems and Prospects of Supercomputer Technologies in the Near Future”, Her. Russ. Acad. Sci., 88:6 (2018), 448  
35. Vladislav Balashov, Evgeny Savenkov, “Numerical simulation of multiphase fows within complex domains with wetting efects”, J. Phys.: Conf. Ser., 1141 (2018), 012088