ライブラリ登録: Guest
International Journal for Multiscale Computational Engineering

年間 6 号発行

ISSN 印刷: 1543-1649

ISSN オンライン: 1940-4352

The Impact Factor measures the average number of citations received in a particular year by papers published in the journal during the two preceding years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) IF: 1.4 To calculate the five year Impact Factor, citations are counted in 2017 to the previous five years and divided by the source items published in the previous five years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) 5-Year IF: 1.3 The Immediacy Index is the average number of times an article is cited in the year it is published. The journal Immediacy Index indicates how quickly articles in a journal are cited. Immediacy Index: 2.2 The Eigenfactor score, developed by Jevin West and Carl Bergstrom at the University of Washington, is a rating of the total importance of a scientific journal. Journals are rated according to the number of incoming citations, with citations from highly ranked journals weighted to make a larger contribution to the eigenfactor than those from poorly ranked journals. Eigenfactor: 0.00034 The Journal Citation Indicator (JCI) is a single measurement of the field-normalized citation impact of journals in the Web of Science Core Collection across disciplines. The key words here are that the metric is normalized and cross-disciplinary. JCI: 0.46 SJR: 0.333 SNIP: 0.606 CiteScore™:: 3.1 H-Index: 31

Indexed in

Numerical Solutions of Some Diffuse Interface Problems: The Cahn-Hilliard Equation and the Model of Thomas and Windle

巻 7, 発行 6, 2009, pp. 523-543
DOI: 10.1615/IntJMultCompEng.v7.i6.40
Get accessGet access

要約

We consider partial differential equations with a suddenly changing parameter. The equations that we study are the Cahn-Hilliard equation, for binary and multicomponent mixtures (i.e., vector Cahn-Hilliard equations), and a stress-enhanced diffusion equation. Numerical strategies to solve these equations are analyzed in terms of discretization and time integration. Results are presented and form the basis for further research. Next to the numerical analysis, we consider some analytic properties such as mass conservation and decrease of energy.

参考
  1. Thornton, K., Ågren, J., and Voorhees, P. W., Modelling the Evolution of Phase Boundaries in Solids at the Meso- and Nano-Scales. DOI: 10.1016/j.actamat.2003.08.008

  2. Ritger, P. L., and Peppas, N. A., Transport of Penetrants in the Macromolecular Structure of Coals. DOI: 10.1016/0016-2361(87)90130-X

  3. Hui, C. Y., Wu, K. C., Lasky, R. C., and Kramer, E. J., Case-II Diffusion in Polymers. I Transient Swelling. DOI: 10.1063/1.338287

  4. Hui, C. Y., Wu, K. C., Lasky, R. C., and Kramer, E. J., Case-II Diffusion in Polymers. II Steady-State Front Motion. DOI: 10.1063/1.338288

  5. Murray, W. D., and Landis, F., Numerical and Machine Solutions of Transient Heat Conduction Problems Involving Freezing and Melting.

  6. Crusius, S., Inden, G., Knoop, U., Höglund, L., and Å gren, J., On the Numerical Treatment of Moving Boundary Problems.

  7. Segal, A., Vuik, C., and Vermolen, F. J., A Conserving Discretization for the Free Boundary in a Two-Dimensional Stefan Problem. DOI: 10.1006/jcph.1998.5900

  8. Osher, S., and Sethian, J. A., Fronts Propagating with Curvature-Dependent Speed. DOI: 10.1016/0021-9991(88)90002-2

  9. Chen, S., Merriman, B., Osher, S., and Smereka, P., A Simple Level-Set Method for Solving Stefan Problems. DOI: 10.1006/jcph.1997.5721

  10. Almgren, R., Variational Algorithms and Pattern Formation in Dendritic Solidification. DOI: 10.1016/S0021-9991(83)71112-5

  11. Schmidt, A., Approximation of Crystalline Dendritic Growth in Two Space Dimensions.

  12. Javierre, E., Vuik, C., Vermolen, F. J., and van der Zwaag, S., A Comparison of Numerical Models for One-Dimensional Stefan Problems. DOI: 10.1016/j.cam.2005.04.062

  13. Van der Waals, J. D., The Thermodynamic Theory of Capillarity under the Hypothesis of a Continuous Variation of Density. DOI: 10.1007/BF01011514

  14. Cahn, J. W., and Hilliard, J. E., Free Energy of a Non-Uniform System. I. Interfacial Energy. DOI: 10.1063/1.1744102

  15. Metallurgical and Thermochemical Databank, National Physical Laboratory.

  16. Wise, S. M., Lowengrub, J. S., Friboes, H. B., and Cristini, V., Three-Dimensional Multispecies Nonlinear Tumor Growth – 1: Model and Numerical Method. DOI: 10.1016/j.jtbi.2008.03.027

  17. Macklin, P., and Lowengrub, J., Nonlinear Simulation of the Effect of Microenvironment on Tumor Growth. DOI: 10.1016/j.jtbi.2006.12.004

  18. Elliott, C. M., and Garcke, H., On the Cahn-Hilliard Equation with Degenerate Mobility. DOI: 10.1137/S0036141094267662

  19. Temam, R., Infinite Dimensional Dynamical Systems in Mechanics and Physics.

  20. Barrett, J. W., Blowey, J. F., and Garcke, H., Finite Element Approximation of the Cahn-Hilliard Equation with Degenerate Mobility. DOI: 10.1137/S0036142997331669

  21. Chan, P. K., and Rey, A. D., A Numerical Method for the Nonlinear Cahn-Hilliard Equation with Nonperiodic Boundary Conditions. DOI: 10.1016/0927-0256(94)00076-O

  22. Wells, G. N., Kuhl, E., and Garakipati, K., A Discontinuous Galerkin Method for the Cahn- Hilliard Equation. DOI: 10.1016/j.jcp.2006.03.010

  23. Ceniceros, H. D., and Roma, A. M., A Nonstiff, Adaptive Mesh Refinement-Based Method for the Cahn-Hilliard Equation. DOI: 10.1016/j.jcp.2007.02.019

  24. Garcke, H., Rumpf, M., and Weikard, U., The Cahn-Hilliard Equation with Elasticity: Finite Element Approximation and Qualitative Studies.

  25. Garcke, H., Maier-Paape, S., and Weikard, U., Spinodal Decomposition in the Presence of Elastic Interactions. DOI: 10.1007/978-3-642-55627-2_32

  26. Cueto-Felgueroso, L., and Peraire, J., A Time- Adaptive Finite Volume Method for the Cahn-Hilliard and Kuramoto-Sivashinsky Equations. DOI: 10.1016/j.jcp.2008.07.024

  27. Elliott, C. M., and Garcke, H., Diffusional Phase Transitions in Multicomponent Systems with a Concentration Dependent Mobility Matrix. DOI: 10.1016/S0167-2789(97)00066-3

  28. Eyre, D. J., Systems of Cahn-Hilliard Equations. DOI: 10.1137/0153078

  29. Maier-Paape, S., Stoth, B., and Wanner, T., Spinodal Decomposition for Multicomponent Cahn-Hilliard Systems. DOI: 10.1023/A:1018687811688

  30. Mikelic, A., and Bruining, J., Analysis of Model Equations for Stress-Enhanced Diffusion in Coal Layers. Part I: Existence of a Weak Solution.

  31. Pego, R. L., Front Migration in the Nonlinear Cahn-Hilliard Equation. DOI: 10.1098/rspa.1989.0027

  32. Mauri, R., Shinnar, R., and Triantafyllou, G., Spinodal Decomposition in Binary Mixtures. DOI: 10.1103/PhysRevE.53.2613

  33. Lowengrub, J., and Truskinovski, L., Quasi- Incompressible Cahn-Hilliard Fluids and Topological Transitions. DOI: 10.1098/rspa.1998.0273

  34. Verschueren, M., A Diffuse-Interface Model for Structure Development in Flow.

  35. Ubachs, R. L. J. M., Schreurs, P. J. G., and Geers, M. G. D., A Nonlocal Diffuse Interface Model for Microstructural Evolution of Tin- Lead Solder. DOI: 10.1016/j.jmps.2004.02.002

  36. Kim, J., A Diffuse-Interface Model for Axi-Symmetric Immiscible Two-Phase Flow. DOI: 10.1016/j.amc.2003.11.020

  37. Andersson, D. M., McFadden, G. B., and Wheeler, A. A., Diffuse-Interface Methods in Fluid Mechanics. DOI: 10.1146/annurev.fluid.30.1.139

  38. Mackenzie, J. A., and Robertson, M. L., A Moving Mesh Method for the Solution of the One-Dimensional Phase-Field Equations. DOI: 10.1006/jcph.2002.7140

  39. Burman, E., Picasso, M., and Rappaz, J., Analysis and Computation of Dendritic Growth in Binary Alloys Using a Phase-Field Model. DOI: 10.1007/978-3-642-18775-9_18

  40. Cheng, X. L., Han,W., and Huang, H. C., Some Mixed Finite Element Methods for Biharmonic Equation. DOI: 10.1016/S0377-0427(99)00342-8

  41. Gholami-Ghorashoo, M., Finite Element Analysis of Cahn-Hilliard Equations.

  42. de Mello, E. V. L., and Teixeira da Silveira Filho, O., Numerical Study of the Cahn-Hilliard Equation in One, Two and Three Dimensions. DOI: 10.1016/j.physa.2004.08.076

  43. Eyre, D. J., An Unconditionally Stable One Step Scheme for Gradient Systems.

  44. He, Y., Liu, Y., and Tang, T., On Large Time-Stepping Methods for the Cahn-Hilliard Equation. DOI: 10.1016/j.apnum.2006.07.026

  45. Elliott, C. M., French, D. A., and Milner, F. A., A Second Order Splitting Method for the Cahn-Hilliard Equation. DOI: 10.1007/BF01396363

  46. Stoth, B. E. E., Convergence of the Cahn-Hilliard Equation to the Mullins-Sekerka Problem in Spherical Geometry.

によって引用された
  1. Vermolen F. J., Segal A., Gefen A., A pilot study of a phenomenological model of adipogenesis in maturing adipocytes using Cahn–Hilliard theory, Medical & Biological Engineering & Computing, 49, 12, 2011. Crossref

  2. Gharasoo Mehdi, Babaei Masoud, Haeckel Matthias, Simulating the chemical kinetics of CO2-methane exchange in hydrate, Journal of Natural Gas Science and Engineering, 62, 2019. Crossref

  3. Boma Wilcox, Wang Qinguy, Abiodun Ayodeji, A Numerical Implementation of the Finite-Difference Algorithm for solving Conserved Cahn–Hilliard Equation, Journal of Physics: Conference Series, 1936, 1, 2021. Crossref

  4. Deng Hang, Gharasoo Mehdi, Zhang Liwei, Dai Zhenxue, Hajizadeh Alireza, Peters Catherine A., Soulaine Cyprien, Thullner Martin, Van Cappellen Philippe, A perspective on applied geochemistry in porous media: Reactive transport modeling of geochemical dynamics and the interplay with flow phenomena and physical alteration, Applied Geochemistry, 146, 2022. Crossref

Begell Digital Portal Begellデジタルライブラリー 電子書籍 ジャーナル 参考文献と会報 リサーチ集 価格及び購読のポリシー Begell House 連絡先 Language English 中文 Русский Português German French Spain