A regularized isothermal phase-field model of two-phase solid–fluid mixture and its spatial dissipative discretization equations

References

[1] D. M. Anderson, G. B. McFadden, and A. A. Wheeler, Diffuse-interface methods in fluid mechanics. Annu. Rev. Fluid Mech. 30 (1998), 139–165.10.6028/NIST.IR.6018Search in Google Scholar

[2] R. W. Anderson, V. A. Dobrev T. V. Kolev, R. N. Rieben, and V. Z. Tomov, High order multi-material ALE hydrodynamics. SIAM J. Sci. Comput. 40 (2018), B32–B58.10.1137/17M1116453Search in Google Scholar

[3] V. A. Balashov and E. B. Savenkov, Quasi-hydrodynamic model of multiphase fluid flows taking into account phase interaction. J. Appl. Mech. Tech. Phy. 59 (2018), 434–444.10.1134/S0021894418030069Search in Google Scholar

[4] V. A. Balashov and E. B. Savenkov, Regularized isothermal phase field model of two-component two-phase compressible fluid and its one-dimensional discritization. Diff. Equat. 56 (2020), No. 7, 857–871.10.1134/S0012266120070058Search in Google Scholar

[5] V. Balashov, A. Zlotnik, and E. Savenkov, Analysis of a regularized model for the isothermal two-component mixture with the diffuse interface. Russ. J. Numer. Anal. Math. Model. 32 (2017), 347–358.10.1515/rnam-2017-0033Search in Google Scholar

[6] V. Balashov, E. Savenkov, and A. Zlotnik, Numerical method for 3D two-component isothermal compressible flows with application to digital rock physics. Russ. J. Numer. Anal. Math. Model. 34 (2019), 1–13.10.1515/rnam-2019-0001Search in Google Scholar

[7] V. A. Balashov and E. B. Savenkov, Thermodynamically consistent spatial discretization of the one- dimensional regularized system of the Navier–Stokes–Cahn–Hilliard equations. J. Comput. Appl. Math. 372 (2020), 112743.10.1016/j.cam.2020.112743Search in Google Scholar

[8] V. Balashov and A. 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 (2021), No. 3, 33.10.1007/s10915-020-01388-6Search in Google Scholar

[9] V. Balashov and A. Zlotnik, An energy dissipative spatial discretization for the regularized compressible Navier–Stokes–Cahn–Hilliard system of equations. Math. Model. Anal. 25 (2020), No. 1, 110–129.10.3846/mma.2020.10577Search in Google Scholar

[10] V. Balashov and A. Zlotnik, An energy dissipative semi-discrete finite-difference method on staggered meshes for the 3D compressible isothermal Navier–Stokes–Cahn–Hilliard equations. J. Comput. Dyn. 7 (2020), No. 2, 291–312.10.3934/jcd.2020012Search in Google Scholar

[11] J. Bałdyga, Mixing and fluid dynamics effects in particle precipitation processes. Kona Powder Part. J. 33 (2016), 127–149.10.14356/kona.2016021Search in Google Scholar

[12] B. N. Chetverushkin, Kinetic Schemes and Quasi-Gas Dynamic System of Equations. CIMNE, Barcelona, 2008.Search in Google Scholar

[13] A. Demianov, O. Dinariev, and N. Evseev, Introduction to the Density Functional Method in Hydrodynamics. Fizmatlit, Moscow (2014) (in Russian).Search in Google Scholar

[14] O. Y. Dinariev and N. V. Evseev, Description of viscous-fluid flows with a moving solid phase in the density-functional theory. J. Engrg. Phys. Thermophys. 80 (2007), 918–926.10.1007/s10891-007-0123-8Search in Google Scholar

[15] T. G. Elizarova, Quasi-Gas Dynamic Equations. Springer, Berlin–Heidelberg–New York, 2009.10.1007/978-3-642-00292-2Search in Google Scholar

[16] N. Favrie, S. L. Gavrilyuk, and R. Saurel, Solid–fluid diffuse interface model in cases of extreme deformations. J. Comput. Phys. 228 (2009), No. 16, 6037–6077.10.1016/j.jcp.2009.05.015Search in Google Scholar

[17] S. K. Godunov and E. I. Romenskii, Elements of Continuum Mechanics and Conservation Laws. Springer, Boston, 2003.10.1007/978-1-4757-5117-8Search in Google Scholar

[18] S. R. de Groot and P. Mazur, Non-equilibrium Thermodynamics. Dover Publications, New York, 1984.Search in Google Scholar

[19] D. Jamet, D. Torres, and J. U. Brackbill, On the theory and computation of surface tension: the elimination of parasitic currents through energy conservation in the second-gradient method. J. Comput. Phys. 182 (2002), 262–276.10.1006/jcph.2002.7165Search in Google Scholar

[20] K. Koga and J. O. Indekeu, Three-phase equilibria in density-functional theory: Interfacial tensions. J. Chem. Phys. 150 (2019), No. 16, 164701.10.1063/1.5091599Search in Google Scholar PubMed

[21] M. M. Krasnov, Operator library for solving multidimensional mathematical physics problems on CUDA. Matem. Mod., 27 (2015), No. 3, 109–120 (in Russian).Search in Google Scholar

[22] M. M. Krasnov, P. A. Kuchugov, M. E. Ladonkina, and V. F. Tishkin, Discontinuous Galerkin method on three-dimensional tetrahedral grids: Using the operator programming method. Math. Models. Comput. Simul., 9 (2017), No. 5, 529–543.10.1134/S2070048217050064Search in Google Scholar

[23] C. Liu and N. Walkington, An Eulerian description of fluids containing visco-elastic particles. Arch. Rational Mech. Anal. 159 (2001), No. 3, 229–252.10.1007/s002050100158Search in Google Scholar

[24] J. Liu, G. Amberg, and M. Do-Quang, Diffuse interface method for a compressible binary fluid. Phys. Rev. E. 93 (2016), No. 1, 013121.10.1103/PhysRevE.93.013121Search in Google Scholar PubMed

[25] J. Lowengrub and L. Truskinovsky, Quasi-incompressible Cahn–Hilliard fluids and topological transitions. Proc. Roy. Soc. Lond. Ser. A. 454 (1998), 2617–2654.10.1098/rspa.1998.0273Search in Google Scholar

[26] D. Mokbel, H. Abels, and S. Aland, A phase-field model for fluid-structure interaction. J. Comput. Phys. 372 (2018), 823–840.10.1016/j.jcp.2018.06.063Search in Google Scholar

[27] N. Provatas and K. Elde, Phase-field Methods in Material Science and Engineering. Willey-VCH, Weinheim, 2010.10.1002/9783527631520Search in Google Scholar

[28] E. I. Romenskii, E. B. Lys’, V. A. Cheverda, and M. I. Epov, Dynamics of deformation of an elastic medium with initial stresses. J. Appl. Mech. Tech. Phys. 58 (2017), 914–923.10.1134/S0021894417050182Search in Google Scholar

[29] W. Boscheri, M. Dumbser, M. Ioriatti, I. Peshkov, and E. Romenski, A structure-preserving staggered semi-implicit finite volume scheme for continuum mechanics. J. Comput. Phys. 424 (2021), 109866.10.1016/j.jcp.2020.109866Search in Google Scholar

[30] R. J. Seager, A. J. Acevedo, F. Spill, and M. H. Zaman, Solid dissolution in a fluid solvent is characterized by the interplay of surface area-dependent diffusion and physical fragmentation. Sci. Rep. 8 (2018), No. 1, 7711.10.1038/s41598-018-25821-xSearch in Google Scholar PubMed PubMed Central

[31] L. I. Sedov, A Course in Continuum Mechanics. Volume I. Wolters–Noordhoff, Groningen, 1971.Search in Google Scholar

[32] Yu. V. Sheretov, Continuum Dynamics under Spatiotemporal Averaging. R&C Dynamics. Moscow–Izhevsk, 2009 (in Russian).Search in Google Scholar

[33] K. Sugiyama, S. Ii, K. Shimizu, S. Noda, and S. Takagi, A full Eulerian method for fluid-structure interaction problems. Procedia IUTAM. 20 (2017), 159–166.10.1016/j.piutam.2017.03.022Search in Google Scholar

[34] K. Sugiyama, S. Ii, S. Takeuchi, S. Takagi, and Y. Matsumoto, A full Eulerian finite difference approach for solving fluid-structure coupling problems. J. Comput. Phys. 230 (2011), 596–627.10.1016/j.jcp.2010.09.032Search in Google Scholar

[35] M. M. Villone and P. L. Maffettone, Dynamics, rheology, and applications of elastic deformable particle suspensions: a review. Rheol. Acta. 58 (2019), 109–130.10.1007/s00397-019-01134-2Search in Google Scholar

[36] T. Wick, Fully Eulerian fluid-structure interaction for time-dependent problems. Comput. Methods. Appl. Mech. Engrg. 255 (2013), 14–26.10.1016/j.cma.2012.11.009Search in Google Scholar

[37] P. Yue, C. Zhou, and J. J. Feng, Spontaneous shrinkage of drops and mass conservation in phase-field simulations. J. Comput. Phys. 223 (2007), No. 1, 1–9.10.1016/j.jcp.2006.11.020Search in Google Scholar

[38] X. Zhao and Q. Wang, A second order fully-discrete linear energy stable scheme for a binary compressible viscous fluid model. J. Comput. Phys. 395 (2019), 382–409.10.1016/j.jcp.2019.06.030Search in Google Scholar

[39] A. A. Zlotnik and T. A. Lomonosov, Conditions for L²-dissipativity of linearized explicit difference schemes with regularization for 1D barotropic gas dynamics equations. Comput. Math. Math. Phys. 59 (2019), 452–464.10.1134/S0965542519030151Search in Google Scholar

[40] A. A. Zlotnik and T. A. Lomonosov, On L²-dissipativity of a linearized explicit finite-difference scheme with quasi-gasdynamic regularization for the barotropic gas dynamics system of equations. Dokl. Math. 101 (2020), 198–204.10.1134/S1064562420030229Search in Google Scholar