### AIMS Mathematics

2019, Issue 3: 648-662. doi: 10.3934/math.2019.3.648
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. ###### 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 1.427 1.6

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