论文标题
RBF-FD离散化在分散但交错节点上的Navier-Stokes方程
RBF-FD discretization of the Navier-Stokes equations on scattered but staggered nodes
论文作者
论文摘要
使用交错的节点布局和径向基函数函数 - 限制差异（RBF-FD）来求解不可压缩的Navier-Stokes方程。具有多项式增强（pHS+poly）的多谐波花纹（PHS）用于构建全局分化矩阵。系统的参数研究确定了模板大小，pHS指数和多项式程度的组合，从而最大程度地减少了散射节点上波浪状测试函数的截断误差。经典修改的波数分析扩展到异质节点分布的RBF-FDS，并用于确认所选28点模板的准确性与光谱样，六阶Padé-Padé-Padé-type有限差异相当。在两个基准问题上证明了Navier-Stokes Solver，在雷诺数制度中的盖子驱动腔中的内部流量$ 10^2 \ leq $ req $ re $ \ re $ \ leq10^4 $，以及在RE = 100和200的圆柱周围的开放流量。使用网格和谨慎的组合，比以前的稳定组合更加稳定地构成，以相比，更稳定的模拟量相比，在稳定的组合中，在稳定的组合中，逐步定期在稳定的模拟，在RBF-FD模具，在实心壁附近没有特殊处理，而无需过度粘度或其他正规化手段。
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 $10^2\leq$Re$\leq10^4$, 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.
