Numerical simulation is the primary approach to evaluate the complex solidification behavior for the continuous casting (CC) process, in which the methods based on the mesh and topology technique have been widely used to solve field variables. For the traditional techniques, such as the finite difference, finite element, and boundary element methods, it is arduous or even impossible to deal with complicated problems that involve multiphase coupling, interface tracking/reconstruction, and self-adaptation due to the inherent weaknesses in the grid structure and mesh dependence. Hence, the present work explores a meshless calculation method for the two-dimensional unsteady heat-transfer problem and proposes an element-free Galerkin (EFG) model for solving heat transfer inside the CC mold based on the moving least-squares approximation. The temperature functions are approximated and constructed by a linear basis and cubic spline weight function over a set of rectangular supporting domain; then, the discrete heat-transfer governing equation based on the EFG method is deduced. The heat flux measured in the real casting process is set as the boundary condition to calculate the nonuniform solidification of the round billet. The calculated results demonstrate that the shell thickness is consistent with that obtained by the square root law of solidification. In addition, the high heat flux region near the meniscus directly determines the growth characteristics of the initial billet shell, which ultimately results in the overall nonuniformity of the shell. The EFG method has the characteristics of fast convergence, high computational accuracy, and great discrete flexibility; it also provides a novel and effective approach for subsequent thermomechanical coupling and crack propagation analysis in the CC process.

中文翻译：

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连铸圆坯不均匀传热/凝固行为的无网格法

数值模拟是评估连铸 (CC) 过程复杂凝固行为的主要方法，其中基于网格和拓扑技术的方法已广泛用于求解场变量。对于传统的有限差分法、有限元法、边界元法等，由于其固有的弱点，很难甚至无法处理涉及多相耦合、界面跟踪/重建和自适应等复杂问题。网格结构和网格依赖性。因此，目前的工作探索了二维非定常传热问题的无网格计算方法，并提出了一种基于移动最小二乘近似求解 CC 模具内部传热的无单元伽辽金 (EFG) 模型。在一组矩形支撑域上通过线性基和三次样条权重函数来近似和构造温度函数；然后，推导出基于EFG方法的离散传热控制方程。以实际铸造过程中测得的热通量为边界条件，计算圆坯不均匀凝固。计算结果表明，壳厚度与凝固平方根定律得到的一致。此外，弯液面附近的高热通量区域直接决定了初始坯壳的生长特性，最终导致壳的整体不均匀性。EFG方法具有收敛速度快、计算精度高、离散灵活性大的特点；