Geodesic
Numerical simulation of unstable processes in phase decomposition problem
Matematičeskoe modelirovanie, Tome 14 (2002) no. 2, pp. 27-38.

Voir la notice de l'article provenant de la source Math-Net.Ru

We carry out numerical simulation of phase decomposition processes in binary alloys for a conservative phase field system. For the case $x\in\mathbb R^1$ explicit and implicit difference schemes are proposed. Numerical results illustrate the main stages of the process dynamics: the interface motion, the evolution and bifurcation of a “soliton”, and the motion and bifurcation of an oscillating singularity. 
@article{MM_2002_14_2_a2,
     author = {D. A. Kulagin and G. A. Omel'yanov and N. O. Ordinartseva},
     title = {Numerical simulation of unstable processes in phase decomposition problem},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {27--38},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2002_14_2_a2/}
}
TY  - JOUR
AU  - D. A. Kulagin
AU  - G. A. Omel'yanov
AU  - N. O. Ordinartseva
TI  - Numerical simulation of unstable processes in phase decomposition problem
JO  - Matematičeskoe modelirovanie
PY  - 2002
SP  - 27
EP  - 38
VL  - 14
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2002_14_2_a2/
LA  - ru
ID  - MM_2002_14_2_a2
ER  - 
%0 Journal Article
%A D. A. Kulagin
%A G. A. Omel'yanov
%A N. O. Ordinartseva
%T Numerical simulation of unstable processes in phase decomposition problem
%J Matematičeskoe modelirovanie
%D 2002
%P 27-38
%V 14
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2002_14_2_a2/
%G ru
%F MM_2002_14_2_a2
D. A. Kulagin; G. A. Omel'yanov; N. O. Ordinartseva. Numerical simulation of unstable processes in phase decomposition problem. Matematičeskoe modelirovanie, Tome 14 (2002) no. 2, pp. 27-38. http://geodesic.mathdoc.fr/item/MM_2002_14_2_a2/

[1] G. Caginalp, “A conserved phase field system: implication for kinetic undercooling”, Phis. Rev. B, 38 (1988), 789–891 | DOI

[2] G. Caginalp, “The dynamics of a conserved phase field system: Stefan like, Hele–Shaw and Cahn–Hilliard models asymptotic limits”, IMA J. Appl. Math., 44 (1990), 77–94 | DOI | MR | Zbl

[3] A. Novick-Cohen, “The nonlinear Cahn–Hilliard equation: transition from spinodal decomposition to nuclear behavior”, J. Stat. Phys., 38:3–4 (1985), 707–722 | DOI

[4] V. G. Danilov, G. A. OmeVanov, E. V. Radkevich, “Soliton-type asymptotic solution of the conserved phase field system”, Portugaliae Mathematica, 53:4 (1996), 471–501 | MR | Zbl

[5] V. G. Danilov, G. A. Ome'anov, E. V. Radkevich, “Tahn-type asymptotic solution of the conserved phase field system”, Adv. in. Math. Sc. Appl., 8:21 (1998) | MR | Zbl

[6] V. G. Danilov, G. A. Ome'anov, “Propagation of singularities and related problems of solidification”, Matematichki Vesnik, 49:3–4 (1997), 143–150 | MR | Zbl

[7] A. A. Samarskii, Teoriya raznostnykh skhem, Nauka, M., 1977 | MR | Zbl

[8] P. Rouch, Vychislitelnaya gidrodinamika, Mir, M., 1980 | Zbl

[9] S. Z. Burstein, E. L. Rubin, “Difference methods for the inviscid and viscous equations of a compressible gas”, J. of Comput. Phys., 2 (1967), 178–196 | DOI

[10] E. C. Nikolaev, A. A. Samarskii, Metody resheniya setochnykh uravnenii, Nauka, M., 1978 | MR