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A stabilized RBF finite difference method for convection dominated flows over meshfree nodes

机译：无网格节点上对流主导流的稳定RBF有限差分法

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摘要

In this paper, a stabilized solution scheme is presented for solving highly convective flow equations on meshfree nodal distribution. The stabilized terms are obtained by considering higher order approximation of governing differential equations over finite control volume while applying force and momentum balance. Spatial derivatives, of resulting flow equations, are treated with Radial Basis Functions in Finite Difference Method (RBF-FD) over meshfree nodal cloud. The characteristic length, for applying equilibrium of forces and momentum, is proposed to be a function of Reynolds number and flow velocity. Performance and accuracy of the proposed scheme is tested for 1-D Convection-Diffusion equations. Numerical tests are conducted for initial conditions having step as well as uniformly varying field variables. The scheme is found to be effective in suppressing the non-physical numerical fluctuations associated with convection dominated flows. Accuracy of the solution with stabilized term is found to be higher than the one without stabilization. The solution scheme is also used for flow around static NACA0012 airfoil at Re = 10, 000. The stabilization term is found to effectively suppress the numerical oscillation when compared to non-stabilized scheme.
机译：本文提出了一种稳定的求解方案，用于求解无网格节点分布上的高对流流动方程。通过在施加力和动量平衡的同时考虑有限控制体积上的控制微分方程的更高阶逼近来获得稳定项。用无差结云上的有限差分法（RBF-FD）中的径向基函数处理所得流量方程的空间导数。为了施加力和动量的平衡，特征长度被提出为雷诺数和流速的函数。对一维对流扩散方程测试了该方案的性能和准确性。对具有阶跃以及均匀变化的场变量的初始条件进行数值测试。发现该方案在抑制与对流占主导的流动相关的非物理数值波动方面是有效的。发现具有稳定项的解决方案的准确性高于没有稳定项的解决方案。该解决方案还用于Re = 10，000的静态NACA0012机翼周围的流动。与非稳定方案相比，发现稳定项有效抑制了数值振荡。

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