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

机译：用局部无网格技术解决二元合金的凝固问题

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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区域内的凝固。引入了质量，能量，动量和物种转移的耦合体积平均控制方程作为控制系统。相的性质通过杠杆凝固法则解决，多孔糊状区中的流体动力学通过达西力建模，并且假定液相表现为不可压缩的牛顿流体。熔体中的双重扩散效应可以通过热解决的Boussinesq假设进行建模。通过新颖的局部径向基函数配置方法（LRBFCM）求解控制方程。通过使用多二次径向基函数（RBF）并置，可以在重叠的5节点子域上表示所有物理量的字段。从RBF的相应导数中计算出所涉及的字段的一阶和二阶导数。通过显式的时间离散化求解方程，并通过局部压力校正方案计算压力-速度耦合。所表示的无网格方法的优点在于它的简单性，准确性，在2D和3D中的相似编码以及在非均匀节点布置和自适应节点布置中的直接适用性。提出的空间离散化技术显示了一些方便的属性和升级的可能性，同时保持简单且CPU效率极高。另一方面，完全本地的求解过程使实现和并行化变得简单（无需求解大型方程组）。

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