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Solution of solidification of a binary alloy by a local meshless technique

机译：通过局部无网格技术凝固二元合金的凝固

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摘要

The present paper deals with the numerical simulation of a multiphase system. The solidification of a binary alloy in a rectangular domain is considered. Coupled volume averaged governing equations for mass, energy, momentum and species transfer are introduced as a governing system. The phase properties are resolved from the Lever solidification rule, the fluid dynamics in the porous mushy zone is modeled by a Darcy force and the liquid phase is assumed to behave like an incompressible Newtonian fluid. Double diffusive effects in the melt are modeled by the thermo-solutal Boussinesq hypothesis. The governing equations are solved by the novel Local Radial Basis Function Collocation Method (LRBFCM). The fields of all physical quantities are represented on overlapping 5-noded sub-domains through collocation by using multiquadrics Radial Basis Functions (RBF). The involved first and second derivatives of the fields are calculated from the respective derivatives of the RBFs. The equations are solved through explicit temporal discretization and the pressure-velocity coupling is calculated through a local pressure correction scheme. The advantages of the represented meshless approach are its simplicity, accuracy, similar coding in 2D and 3D, and straightforward applicability in non-uniform node arrangements and adaptive node arrangements. The presented spatial discretization technique shows several convenient properties and possibilities for upgrade, whereas stays simple and extremely CPU efficient. On the other hand, the completely local solution procedure makes the implementation and parallelization straightforward (without solving big systems of equations).
机译：本文涉及多相系统的数值模拟。考虑二元合金在矩形结构域中的凝固。将耦合体积平均用于质量，能量，动量和物种转移的控制方程作为管理系统。从杠杆凝固规则解析相位性质，多孔糊状区中的流体动力学由达西力建模，并且假设液相表现得像不可压缩的牛顿液一样。熔体中的双重扩散效果由热溶解的Boussinesq假设进行建模。通过新颖的局部径向基函数搭配方法（LRBFCM）解决了管理方程。所有物理量的字段通过使用多氖性径向基函数（RBF）来表示通过搭配重叠的5点点向子域。域的涉及的第一和第二衍生物由RBF的各个衍生物计算。通过明确的时间离散化来解决方程，并且通过局部压力校正方案计算压力 - 速度耦合。所代表的无网格方法的优点是其简单，精度，在2D和3D中类似的编码，以及非均匀节点布置和自适应节点布置中的直接适用性。呈现的空间离散化技术显示出几种方便的升级性能和可能性，而保持简单且极其CPU高效。另一方面，完全本地解决方案程序直接实现实施和并行化（不解决方程的大系统）。

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