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

Costică Moroşanu; Costică Moroşanu

doi:10.3934/math.2019.3.648

AIMS Mathematics

2019, Volume 4, Issue 3: 648-662. doi: 10.3934/math.2019.3.648

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

Costică Moroşanu ^,

“Al. I. Cuza” University, Department of Mathematics, 700506, Iaşi, Romania

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.
- nonlinear PDE of parabolic type,
- reaction-diffusion equations,
- fractional steps method,
- finite element method,
- performance of numerical algorithms,
- thermodynamics,
- phase-changes
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

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Abstract

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.

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