RBF-FD discretization of the Navier-Stokes equations on scattered but staggered nodes
RBF-FD discretization of the Navier-Stokes equations on scattered but staggered nodes
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DOI：
10.1016/j.jcp.2022.111756
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发表时间：
2022-06
期刊：
影响因子：
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通讯作者：
Tianyi Chu;O. Schmidt
中科院分区：
文献类型：
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作者：
Tianyi Chu;O. Schmidt
提出了一种用交错节点布局和径向基函数-有限差分(RBF-FD)求解不可压N-S方程的半隐式分数步方法。采用多项式增广多项式多项式样条(PHS+POLY)构造全局微分矩阵。一项系统的参数研究确定了模板大小、PHS指数和多项式次数的组合，以最小化分散节点上的波状测试函数的截断误差。将经典的修正波数分析推广到非均匀节点分布的RBF-FDs，并用来验证所选择的28点模板的精度与类似谱的6阶Padé型有限差分的精度相当。在雷诺数为10 2≤Re≤10 4时的盖子驱动空腔内的内部流动，以及在Re=10 0和2 0 0时圆柱体周围的开放流动。网格交错和仔细的参数选择相结合，使用更紧凑的RBF-FD模板，在比以前报告的分辨率低得多的情况下，促进了准确和稳定的模拟，不需要在固体壁上进行特殊处理，也不需要高粘度或其他正则化手段。
A semi-implicit fractional-step method that uses a staggered node layout and radial basis function-finite differences (RBF-FD) to solve the incompressible Navier-Stokes equations is developed. Polyharmonic splines (PHS) with polynomial augmentation (PHS+ poly) are used to construct the global differentiation matrices. A systematic parameter study identifies a combination of stencil size, PHS exponent, and polynomial degree that minimizes the truncation error for a wave-like test function on scattered nodes. Classical modified wavenumber analysis is extended to RBF-FDs on heterogeneous node distributions and used to confirm that the accuracy of the selected 28-point stencil is comparable to that of spectral-like, 6th-order Padé-type finite differences. The Navier-Stokes solver is demonstrated on two benchmark problems, internal flow in a lid-driven cavity in the Reynolds number regime 10 2≤ Re≤ 10 4, and open flow around a cylinder at Re= 100 and 200. The combination of grid staggering and careful parameter selection facilitates accurate and stable simulations at significantly lower resolutions than previously reported, using more compact RBF-FD stencils, without special treatment near solid walls, and without the need for hyperviscosity or other means of regularization.