Эффективный алгоритм решения системы уравнений Аллена-Кана и Кана-Хиллиарда: моделирование процесса спекания
DOI:
https://doi.org/10.26089/NumMet.v23r206Ключевые слова:
спекание, фазовое поле, уравнение Кана-Хиллиарда, уравнение Аллена-КанаАннотация
В работе представлен алгоритм решения системы уравнений Аллена–Кана и Кана–Хиллиарда, которая описывает процесс спекания. Алгоритм не требует значительных по мощности вычислительных ресурсов и позволяет выполнить моделирование процесса спекания большого количества отдельных частиц на вычислительном узле с процессором Intel Xeon E5 2697 v3 и графическим ускорителем NVIDIA K40 за приемлемое время. Проведены эксперименты по моделированию спекания сорбентоподобных структур — упаковок сферических частиц, и на них показана эффективность алгоритма.
Библиографические ссылки
- H. Tanaka, “Sintering of Silicon Carbide and Theory of Sintering,” J. Ceramic Soc. JAPAN 110 (1286), 877-883 (2002).
doi 10.2109/jcersj.110.877 - J. Poetschke, V. Richter, T. Gestrich, and A. Michaelis, “Grain Growth during Sintering of Tungsten Carbide Ceramics,” Int. J. Refract. Met. Hard Mater. 43, 309-316 (2014).
doi 10.1016/j.ijrmhm.2014.01.001 - N. Florin and P. Fennell, “Synthetic CaO-based Sorbent for CO_2 Capture,” Energy Procedia 4, 830-838 (2011).
doi 10.1016/j.egypro.2011.01.126 - Ya. V. Bazaikin, E. G. Malkovich, V. S. Derevschikov, et al., “Evolution of Sorptive and Textural Properties of CaO-based Sorbents during Repetitive Sorption/Regeneration Cycles,” Chem. Eng. Sci. 152, 709-716 (2016).
doi 10.1016/j.ces.2016.06.064 - R. K. Bordia, S.-J. L. Kang, and E. A. Olevsky, “Current Understanding and Future Research Directions at the Onset of the Next Century of Sintering Science and Technology,” J. Am. Ceram. Soc. 100 (6), 2314-2352 (2017).
doi 10.1111/jace.14919 - R. E. White, “An Enthalpy Formulation of the Stefan Problem,” SIAM J. Numer. Anal. 19 (6), 1129-1157 (1982).
https://www.jstor.org/stable/2157200 . Cited April 10, 2022. - A. W. Date, “A Strong Enthalpy Formulation for the Stefan Problem,” Int. J. Heat Mass Transf. 34 (9), 2231-2235 (1991).
doi 10.1016/0017-9310(91)90049-K - D. Tarwidi and S. R. Pudjaprasetya, “Godunov Method for Stefan Problems with Enthalpy Formulations,” East Asian J. Appl. Math. 3 (2), 107-119 (2013).
doi 10.4208/eajam.030513.200513a - S. Molins, D. Trebotich, C. Steefel, and C. Shen, “An Investigation of the Effect of Pore Scale Flow on Average Geochemical Reaction Rates Using Direct Numerical Simulation,” Water Resour. Res. 48 (3) (2012).
doi 10.1029/2011WR011404 - S. Molins, D. Trebotich, L. Yang, et al., “Pore-Scale Controls on Calcite Dissolution Rates from Flow-through Laboratory and Numerical Experiments,” Environ. Sci. Technol. 48 (13), 7453-7460 (2014).
doi 10.1021/es5013438 - C. I. Steefel and A. C. Lasaga, “A Coupled Model for Transport of Multiple Chemical Species and Kinetic Precipitation/Dissolution Reactions with Application to Reactive Flow in Single Phase Hydrothermal Systems,” Am. J. Sci. 294 (5), 529-592 (1994).
doi 10.2475/ajs.294.5.529 - D. Trebotich, M. F. Adams, S. Molins, et al., “High-Resolution Simulation of Pore-Scale Reactive Transport Processes Associated with Carbon Sequestration,” Comput. Sci. Eng. 16 (6), 22-31 (2014).
doi 10.1109/MCSE.2014.77 - X. Li, H. Huang, and P. Meakin, “Level Set Simulation of Coupled Advection-Diffusion and Pore Structure Evolution due to Mineral Precipitation in Porous Media,” Water Resour. Res. 44 (12) (2008).
doi 10.1029/2007WR006742 - X. Li, H. Huang, and P. Meakin, “A Three-Dimensional Level Set Simulation of Coupled Reactive Transport and Precipitation/Dissolution,” Int. J. Heat Mass Transf. 53 (13), 2908-2923 (2010).
doi 10.1016/j.ijheatmasstransfer.2010.01.044 - S. Osher and R. P. Fedkiw, “Level Set Methods: An Overview and Some Recent Results,” J. Comput. Phys. 169 (2), 463-502 (2001).
doi 10.1006/jcph.2000.6636 - S. Marella, S. Krishnan, H. Liu, and H. S. Udaykumar, “Sharp Interface Cartesian Grid Method I: An Easily Implemented Technique for 3D Moving Boundary Computations,” J. Comput. Phys. 210 (1), 1-31 (2005).
doi 10.1016/j.jcp.2005.03.031 - R. Mittal and G. Iaccarino, “Immersed Boundary Methods,” Annu. Rev. Fluid Mech. 37 (1), 239-261 (2005).
doi 10.1146/annurev.fluid.37.061903.175743 - C. S. Peskin, “Flow Patterns around Heart Valves: A Numerical Method,” J. Comput. Phys. 10 (2), 252-271 (1972).
doi 10.1016/0021-9991(72)90065-4 - F. Sotiropoulos and X. Yang, “Immersed Boundary Methods for Simulating Fluid-Structure Interaction,” Prog. Aerosp. Sci. 65, 1-21 (2014).
doi 10.1016/j.paerosci.2013.09.003 - Y.-H. Tseng and J. H. Ferziger, “A Ghost-Cell Immersed Boundary Method for Flow in Complex Geometry,” J. Comput. Phys. 192 (2), 593-623 (2003).
doi 10.1016/j.jcp.2003.07.024 - K. A. Gadylshina, T. S. Khachkova, and V. V. Lisitsa, “Numerical Modeling of Chemical Interaction between a Fluid and Rocks,” Vychisl. Metody Program. 20 (4), 457-470 (2019).
doi 10.26089/NumMet.v20r440 - D. Prokhorov, V. Lisitsa, T. Khachkova, et al., “Topology-Based Characterization of Chemically-Induced Pore Space Changes Using Reduction of 3D Digital Images,” J. Comput. Sci. 58 (2022).
doi 10.1016/j.jocs.2021.101550 - D. P. Munoz, J. Bruchon, F. Valdivieso, and S. Drapier, “Solid-State Sintering Simulation: Surface, Volume and Grain-Boundary Diffusions,” in Proc. ECCOMAS 2012: European Congress on Computational Methods in Applied Sciences and Engineering, Vienna, Austria, September 10-14, 2012 ,
https://www.researchgate.net/publication/235673306_Solid-state_sintering_simulation_Surface_volume_and_grain-boundary_diffusions . Cited April 10, 2022. - P. Smereka, “Semi-Implicit Level Set Methods for Curvature and Surface Diffusion Motion,” J. Sci. Comput. 19 (1-3), 439-456 (2003).
doi 10.1023/A: 1025324613450 - N. Moelans, B. Blanpain, and P. Wollants, “An Introduction to Phase-Field Modeling of Microstructure Evolution,” Calphad 32 (2), 268-294 (2008).
doi 10.1016/j.calphad.2007.11.003 - J. W. Cahn and J. E. Hilliard, “Free Energy of a Nonuniform System. I. Interfacial Free Energy,” J. Chem. Phys. 28 (2), 258-267 (1958).
doi 10.1063/1.1744102 - S. M. Allen and J. W. Cahn, “Ground State Structures in Ordered Binary Alloys with Second Neighbor Interactions,” Acta Metall. 20 (3), 423-433 (1972).
doi 10.1016/0001-6160(72)90037-5 - Yu. U. Wang, “Computer Modeling and Simulation of Solid-State Sintering: A Phase Field Approach,” Acta Mater. 54 (4), 953-961 (2006).
doi 10.1016/j.actamat.2005.10.032 - S. G. Kim, D. I. Kim, W. T. Kim, and Y. B. Park, “Computer Simulations of Two-Dimensional and Three-Dimensional Ideal Grain Growth,” Phys. Rev. E 74 (2006).
doi 10.1103/PhysRevE.74.061605 - J. Hötzer, M. Jainta, P. Steinmetz, et al., “Large Scale Phase-Field Simulations of Directional Ternary Eutectic Solidification,” Acta Mater. 93, 194-204 (2015).
doi 10.1016/j.actamat.2015.03.051 - R. Zhang, Z. Chen, W. Fang, and X. Qu, “Thermodynamic Consistent Phase Field Model for Sintering Process with Multiphase Powders,” Trans. Nonferrous Met. Soc. China 24 (3), 783-789 (2014).
doi 10.1016/S1003-6326(14)63126-5 - J. Hötzer, M. Seiz, M. Kellner, et al., “Phase-Field Simulation of Solid State Sintering,” Acta Mater. 164, 184-195 (2019).
doi 10.1016/j.actamat.2018.10.021 - N. Moelans, F. Wendler, and B. Nestler, “Comparative Study of Two Phase-Field Models for Grain Growth,” Comput. Mater. Sci. 46 (2), 479-490 (2009).
doi 10.1016/j.commatsci.2009.03.037 - J. W. Cahn, “On Spinodal Decomposition,” Acta Metall. 9 (9), 795-801 (1961).
doi 10.1016/0001-6160(61)90182-1 - A. Fick, “Ueber Diffusion,” Ann. Phys. 170 (1), 59-86 (1855).
doi 10.1002/andp.18551700105 - Ya. E. Geguzin, Physics of Sintering (Nauka, Moscow, 1984) [in Russian].
- K. Ahmed, J. Pakarinen, T. Allen, and A. El-Azab, “Phase Field Simulation of Grain Growth in Porous Uranium Dioxide,” J. Nucl. Mater. 446 (1-3), 90-99 (2014).
doi 10.1016/j.jnucmat.2013.11.036 - M. A. Spears and A. G. Evans, “Microstructure Development during Final/Intermediate Stage Sintering—II. Grain and Pore Coarsening,” Acta Metall. 30 (7), 1281-1289 (1982).
doi 10.1016/0001-6160(82)90146-8 - C. Shen, Q. Chen, Y. H. Wen, et al., “Increasing Length Scale of Quantitative Phase Field Modeling of Growth-Dominant or Coarsening-Dominant Process,” Scr. Mater. 50 (7), 1023-1028 (2004).
doi 10.1016/j.scriptamat.2003.12.029 - R. M. German, Sintering Theory and Practice (Wiley, New York, 1996).
- Ya. V. Bazaikin, E. G. Malkovich, D. I. Prokhorov, and V. S. Derevschikov, “Detailed Modeling of Sorptive and Textural Properties of CaO-Based Sorbents with Various Porous Structures,” Sep. Purif. Technol. 255 (2021).
doi 10.1016/j.seppur.2020.117746 - B. D. Lubachevsky and F. H. Stillinger, “Geometric Properties of Random Disk Packings,” J. Stat. Phys. 60, 561-583 (1990).
doi 10.1007/BF01025983 - Y.-S. Liu, J. Yi, H. Zhang, et al., “Surface Area Estimation of Digitized 3D Objects Using Quasi-Monte Carlo Methods,” Pattern Recognit. 43 (11), 3900-3909 (2010).
doi 10.1016/j.patcog.2010.06.002 - V. S. Derevschikov, J. V. Veselovskaya, T. Yu. Kardash, et al., “Direct CO_2 Capture from Ambient Air Using K_2CO_3/Y_2O_3 Composite Sorbent,” Fuel 127, 212-218 (2014)
doi 10.1016/j.fuel.2013.09.060
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