Comptes Rendus
Ordinary differential equations/Numerical analysis
Numerical analysis of an isotropic phase-field model with magnetic-field effect
Comptes Rendus. Mathématique, Volume 353 (2015) no. 3, pp. 219-224.

The aim of this letter is to perform the numerical analysis of an isotropic phase-field model for dendritic solidification of a binary alloy subject to an applied magnetic field in an isothermal environment. Precisely, the numerical stability and error analysis of a finite-element-based approximation scheme are performed. The particular example of a nickel–copper (Ni–Cu) binary alloy is considered. The study substantiates a good agreement between the numerical and theoretical results.

Le but de cette note est d'effectuer l'analyse numérique d'un modèle isotrope de champ de phase pour la solidification dendritique d'un alliage binaire sous l'effet d'un champ magnétique appliqué dans un environnement isotherme. Précisément, la stabilité numérique et l'analyse d'erreur du schéma d'approximation éléments finis sont effectuées. L'exemple particulier d'un alliage binaire nickel–cuivre (Ni–Cu) est considéré. L'étude montre un bon accord entre les résultats numériques et théoriques.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2014.12.002

Amer Rasheed 1; Abdul Wahab 2

1 Department of Mathematics, School of Science and Engineering, Lahore University of Management Sciences, Opposite Sector U, DHA, Lahore Cantt 54792, Pakistan
2 Department of Mathematics, COMSATS Institute of Information Technology, G.T. Road, 47040, Wah Cantt., Pakistan
@article{CRMATH_2015__353_3_219_0,
     author = {Amer Rasheed and Abdul Wahab},
     title = {Numerical analysis of an isotropic phase-field model with magnetic-field effect},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {219--224},
     publisher = {Elsevier},
     volume = {353},
     number = {3},
     year = {2015},
     doi = {10.1016/j.crma.2014.12.002},
     language = {en},
}
TY  - JOUR
AU  - Amer Rasheed
AU  - Abdul Wahab
TI  - Numerical analysis of an isotropic phase-field model with magnetic-field effect
JO  - Comptes Rendus. Mathématique
PY  - 2015
SP  - 219
EP  - 224
VL  - 353
IS  - 3
PB  - Elsevier
DO  - 10.1016/j.crma.2014.12.002
LA  - en
ID  - CRMATH_2015__353_3_219_0
ER  - 
%0 Journal Article
%A Amer Rasheed
%A Abdul Wahab
%T Numerical analysis of an isotropic phase-field model with magnetic-field effect
%J Comptes Rendus. Mathématique
%D 2015
%P 219-224
%V 353
%N 3
%I Elsevier
%R 10.1016/j.crma.2014.12.002
%G en
%F CRMATH_2015__353_3_219_0
Amer Rasheed; Abdul Wahab. Numerical analysis of an isotropic phase-field model with magnetic-field effect. Comptes Rendus. Mathématique, Volume 353 (2015) no. 3, pp. 219-224. doi : 10.1016/j.crma.2014.12.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.12.002/

[1] M.D. Anderson; G.B. McFadden; A.A. Wheeler A phase-field model of solidification with convection, Physica D, Volume 135 (2000), pp. 175-194

[2] A. Belmiloudi Method of characteristics and error estimates of the perturbation of given mean flow, Application of Mathematics in Engineering and Business Sozopol, Proc. XXIInd Summer School, 1996, pp. 25-38

[3] M. Grujicic; G. Cao; R.S. Millar Computer modelling of the evolution of dendrite microstructure in binary alloys during non-isothermal solidification, J. Mater. Synth. Process., Volume 10 (2002), pp. 191-203

[4] H.B. Hadid; D. Henry; S. Kaddeche Numerical study of convection in the horizontal Bridgman configuration under the action of a constant magnetic field. Part 1. Two-dimensional flow, J. Fluid Mech., Volume 333 (1997), pp. 23-56

[5] M. Li; T. Takuya; N. Omura; K. Miwa Effects of magnetic field and electric current on the solidification of AZ91D magnesium alloys using an electromagnetic vibration technique, J. Alloys Compd., Volume 487 (2009), pp. 187-193

[6] L.R. Petzold A description of DASSL: a differential/algebraic system solver, IMACS Trans. Sci. Comput. (1983), pp. 65-68

[7] P. Prescott; F. Incropera Magnetically damped convection during solidification of a binary metal alloy, Trans. Amer. Soc. Mech. Eng., Volume 115 (1993), pp. 302-310

[8] J.C. Ramizer; C. Beckermann Examination of binary alloy free dendritic growth theories with a phase-field model, Acta Mater., Volume 53 (2005), pp. 1721-1736

[9] A. Rasheed Dendritic solidification of binary mixtures of metals under the action of magnetic field: modeling, mathematical and numerical analysis, INSA de Rennes, France, 2010 (Ph.D. dissertation)

[10] A. Rasheed; A. Belmiloudi An analysis of the phase-field model for isothermal binary alloy solidification with convection under the influence of magnetic field, J. Math. Anal. Appl., Volume 390 (2012), pp. 244-273

[11] A. Rasheed; A. Belmiloudi Mathematical modelling and numerical simulation of dendrite growth using phase-field method with a magnetic field effect, Commun. Comput. Phys., Volume 14 (2013), pp. 477-508

[12] A. Rasheed; A. Belmiloudi; F. Mahé Dynamics of dendrite growth in a binary alloy with magnetic field affect, Discrete Contin. Dyn. Syst. (2011), pp. 1224-1233 (special issue)

[13] R. Sampath The adjoint method for the design of directional binary alloy solidification processes in the presence of a strong magnetic field, Cornell University, Ithaca, NY, USA, 2001 (Ph.D. dissertation)

[14] E. Süli Convergence and non-linear stability of Lagrange–Galerkin method for the Navier–Stokes equations, Numer. Math., Volume 53 (1988), pp. 459-483

[15] X. Tong; C. Beckermann; A. Kerma; Q. Li Phase-field simulations of dendritic crystal growth in a forced flow, Phys. Rev. E, Volume 63 (2001), p. 061601

[16] J.A. Warren; W.J. Boettinger Prediction of dendritic growth and microsegregation patterns in a binary alloy using the phase-field method, Acta Metall. Mater., Volume 43 (1995), pp. 689-703

Cited by Sources:

Comments - Policy