Research article Topical Sections

Modeling of the continuous casting process of steel via phase-field transition system. Fractional steps method

  • Received: 05 March 2019 Accepted: 16 May 2019 Published: 11 June 2019
  • MSC : 35K55, 35K57, 65M60, 65Y20, 80Axx

  • Here we consider the phase field transition system (a nonlinear system of parabolic type), introduced by G. Caginalp to distinguish between the phases of the material that is involved in the solidification process. On the basis of the convergence of an iterative scheme of fractional steps type, a conceptual numerical algorithm is elaborated in order to approximate the solution of the nonlinear parabolic problem. The advantage of such approach is that the new method simplifies the numerical computations due to its decoupling feature. The finite element method (fem) in 2D is used to deduce the discrete equations and numerical results regarding the physical aspects of solidification process are reported. In order to refer the continuous casting process, the adequate boundary conditions was considered.

    Citation: Costică Moroşanu. Modeling of the continuous casting process of steel via phase-field transition system. Fractional steps method[J]. AIMS Mathematics, 2019, 4(3): 648-662. doi: 10.3934/math.2019.3.648

    Related Papers:

  • Here we consider the phase field transition system (a nonlinear system of parabolic type), introduced by G. Caginalp to distinguish between the phases of the material that is involved in the solidification process. On the basis of the convergence of an iterative scheme of fractional steps type, a conceptual numerical algorithm is elaborated in order to approximate the solution of the nonlinear parabolic problem. The advantage of such approach is that the new method simplifies the numerical computations due to its decoupling feature. The finite element method (fem) in 2D is used to deduce the discrete equations and numerical results regarding the physical aspects of solidification process are reported. In order to refer the continuous casting process, the adequate boundary conditions was considered.


    加载中


    [1] O. Axelson and V. Barker, Finite element solution of boundary value problems, Academic Press, 1984.
    [2] T. Benincasa and C. Moroşanu, Fractional steps scheme to approximate the phase-field transition system with non-homogeneous Cauchy-Neumann boundary conditions, Numer. Func. Anal. Opt., 30 (2009), 199-213. doi: 10.1080/01630560902841120
    [3] G. Caginalp, An analysis of a phase field model of a free boundary, Arch. Ration. Mech. An., 92 (1986), 205-245. doi: 10.1007/BF00254827
    [4] G. Caginalp and X. Chen,Convergence of the phase field model to its sharp interface limits, Eur. J. Appl. Math., 9 (1998), 417-445. doi: 10.1017/S0956792598003520
    [5] O. Cârjă, A. Miranville and C. Moroşanu, On the existence, uniqueness and regularity of solutions to the phase-field system with a general regular potential and a general class of nonlinear and non-homogeneous boundary conditions, Nonlinear Anal-Theor, 113 (2015), 190-208.
    [6] G. Iorga, C. Moroşanu and S. C. Cocindău, Numerical simulation of the solid region via phase field transition system, Metal. Int., 13 (2008), 91-95.
    [7] G. Iorga, C. Moroşanu and I. Tofan, Numerical simulation of the thickness accretions in the secondary cooling zone of a continuous casting machine, Metal. Int., 14 (2009), 72-75.
    [8] N. Kenmochi and M. Niezgόdka, Evolution systems of nonlinear variational inequalities arising from phase change problems, Nonlinear Anal-Theor, 22 (1994), 1163-1180. doi: 10.1016/0362-546X(94)90235-6
    [9] A. Miranville and C. Moroşanu, On the existence, uniqueness and regularity of solutions to the phase-field transition system with non-homogeneous Cauchy-Neumann and nonlinear dynamic boundary conditions, Appl. Math. Model., 40 (2016), 192-207.
    [10] A. Miranville and C. Moroşanu, Analysis of an iterative scheme of fractional steps type associated to the nonlinear phase-field equation with non-homogeneous dynamic boundary conditions, Discrete Cont. Dyn-S, 9 (2016), 537-556. doi: 10.3934/dcdss.2016011
    [11] C. Moroşanu, Approximation of the phase-field transition system via fractional steps method, Numer. Func. Anal. Opt., 18 (1997), 623-648. doi: 10.1080/01630569708816782
    [12] C. Moroşanu, et al., Report Stage II/2006, CEEX program no. 84/2005.
    [13] C. Moroşanu, Fractional steps method for approximation the solid region via phase field transition system, 6-th International Conference APLIMAT2007, Bratislava, 6-9 Feb. 2007.
    [14] C. Moroşanu, et al., Report Stage III/2007, CEEX program no. 84/2005.
    [15] C. Moroşanu, Approximation of the solid region in the continuous casting process of steel via phase-field transition system, 6th European Conference on Continuous Casting, Riccione, Italy, 3-6 Jun., 1-6, 2008.
    [16] C. Moroşanu, Analysis and optimal control of phase-field transition system: Fractional steps methods, Bentham Science Publishers, 2012.
    [17] C. Moroşanu, Qualitative and quantitative analysis for a nonlinear reaction-diffusion equation, ROMAI J., 12 (2016), 85-113.
    [18] C. Moroşanu and A. Croitoru, Analysis of an iterative scheme of fractional steps type associated to the phase-field equation endowed with a general nonlinearity and Cauchy-Neumann boundary conditions, J. Math. Anal. Appl., 425 (2015), 1225-1239. doi: 10.1016/j.jmaa.2015.01.033
    [19] C. Moroşanu, I. Crudu, G. Iorga, et al. Research Concerning the Evolution of Solidification Front via Phase-Field Transition System, CEx05-D11-Prog.no., 84 (2008), IFA Bucharest.
    [20] C. Moroşanu and D. Motreanu, A generalized phase field system, J. Math. Anal. Appl., 237 (1999), 515-540. doi: 10.1006/jmaa.1999.6467
    [21] O. A. Oleinik, A method of solution of the general Stefan problem,.Dokl. Akad. Nauk SSSR, 135 (1960), 1354-1357.
    [22] O. Penrose and P. C. Fife, Thermodynamically consistent models of phase-field type for kinetics of phase transitions, International Symposium on Physical Design, 43 (1990), 44-62.
    [23] L. I. Rubinstein, The Stefan problem, Transl. Math. Monographs, 27, American Mathematical Society, Providence, Rhode Island, 1971.
    [24] R. Temam, Infinite-dimensional dynamical systems in mechanics and physics, Vol. 68.of Applied Mathematical Sciences, Springer-Verlag, New York, second edition, 1997.
    [25] B. G. Thomas, Continuous Casting: Modeling, The Encyclopedia of Advanced Materials, (J. Dantzig, A. Greenwell, J. Mickalczyk, eds.), Pergamon Elsevier Science Ltd., Oxford, UK, 2 (2001), 8p.
  • Reader Comments
  • © 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(4325) PDF downloads(1011) Cited by(6)

Article outline

Figures and Tables

Figures(12)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog