基于无网格伽辽金法的连铸坯凝固计算方法

为考察无网格方法求解铸坯凝固过程的可行性，本文依据移动最小二乘和变分原理，推导并建立了基于无网格伽辽金法的结晶器内铸坯凝固过程二维非稳态传热/凝固数学模型。以小方坯凝固过程为对象，分别采用节点均匀布置、加密布置、随机布置方式，模拟分析了小方坯凝固过程的温度场变化，并将计算结果与参考解、有限元法数值解进行了对比，结果证实无网格伽辽金法在计算精度、自适应性、网格依赖性等方面均优于有限元法。研究结果为无网格方法应用于连铸过程的传热、凝固以及应力/应变行为的数值计算提供参考。 

Calculation of continuous casting billet solidification based on element-free Galerkin method

The mold is the core component of a continuous caster, and the complex metallurgical behavior in the mold is the primary factor determining the quality of continuous casting slabs. The numerical simulation method based on meshing, such as the finite element method, has become an important method to study the complex heat transfer and mechanical behavior in the mold. With in-depth research, the meshing-based numerical simulation method has been found incapable of accurately reconstructing the solidified shell shape of slabs and tracing the liquid-solid phases coexisting region, and addressing some complex problems such as large deformation and crack propagation is difficult. To investigate the feasibility of the meshless method for solving the solidification process of continuous casting billet, according to the moving least square method and variational principle, a two-dimensional unsteady transient heat transfer mathematical model of billet solidification process in mold was established based on element-free Galerkin method. In this work, an arrangement of the uniform, increased density, and randomly distributed nodes was used to calculate the change of temperature field during the billet solidification process. The calculation results of the element-free Galerkin method were compared with the reference solution and the numerical solution of the finite element method. The results show that the element-free Galerkin method outperforms the finite element method in terms of accuracy, adaptability, and mesh-dependence. The study results provide references for applying the meshless method to the numerical calculation of heat transfer, solidification, and stress/strain behaviors in the continuous casting process.