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Simulation of laminar backward facing step flow under magnetic field with explicit local radial basis function collocation method

机译：显式局部径向基函数配置法模拟磁场层流向后步进流

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摘要

The purpose of the present paper is to extend the use of a novel meshless Local Radial Basis Function Collocation Method (LRBFCM) for solving the two-dimensional, steady, laminar flow over a backward facing step under the influence of the Lorentz force. The incompressible Navier-Stokes equations are under the influence of predetermined static magnetic field numerically solved on a non-uniform node arrangement In the numerical procedure, local collocation and Multiquadric Radial Basis Functions (MQ RBF) are used on five-nodded subdomains. The coupling between the pressure and the velocity is made by using Fractional Step Method (FSM). The considered problem is calculated for Reynolds numbers (Re) ranging from 300 to 800, Hartman numbers (Ha) ranging from 0 to 100, and for low magnetic Re_m number. The numerical results demonstrate excellent agreement with previously published data, obtained with the classical numerical methods, such as Finite Volume Method (FVM) and Finite Element Method (FEM). Simplicity of the numerical implementation, accuracy and the absence of the polygonalisation are the main advantages of the LRBFCM.
机译：本文的目的是扩展一种新颖的无网格局部径向基函数配置方法（LRBFCM）来解决在洛伦兹力的作用下向后台阶上的二维，稳定层流。不可压缩的Navier-Stokes方程受到数值求解的非均匀节点排列上预定静磁场的影响。在数值过程中，对五个节点的子域使用局部配位和多二次径向基函数（MQ RBF）。压力和速度之间的耦合是通过使用分数阶跃方法（FSM）进行的。对于范围为300到800的雷诺数（Re），范围为0到100的哈特曼数（Ha）和低磁性Re_m数，计算出所考虑的问题。数值结果表明，与经典数值方法（例如有限体积法（FVM）和有限元方法（FEM））获得的先前发布的数据非常吻合。数值实现的简单性，准确性和不存在多边形化是LRBFCM的主要优点。

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