Derivation of high-order compact finite difference schemes for non-uniform grid using polynomial interpolation
Derivation of high-order compact finite difference schemes for non-uniform grid using polynomial interpolation
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DOI：
10.1016/j.jcp.2004.10.014
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发表时间：
2005-04
影响因子：
4.1
通讯作者：
R. Shukla;X. Zhong
中科院分区：
文献类型：
--
作者：
R. Shukla;X. Zhong
本文利用简单的多项式插值方法，在非均匀网格上导出了任意高阶的一阶导数紧致格式和二阶导数三对角紧致格式（由内部三个二阶导数节点和边界两个二阶导数节点组成）。边界和近边界计划的内部相同的顺序也开发使用多项式插值和一般紧凑的计划在非均匀网格上，它表明，多项式插值是更有效的比传统的方法待定系数的计划系数。由此得到的高阶非均匀格式沿着的边界闭合度可达14阶，在适当拉伸的非均匀网格上是稳定的，从而使更多的网格点聚集在边界附近。研究了高阶非均匀网格格式的稳定性和分辨率特性，并给出了三个数值试验的结果。
In this paper simple polynomial interpolation is used to derive arbitrarily high-order compact schemes for the first derivative and tridiagonal compact schemes for the second derivative (consisting of three second derivative nodes in the interior and two on the boundary) on non-uniform grids. Boundary and near boundary schemes of the same order as the interior are also developed using polynomial interpolation and for a general compact scheme on a non-uniform grid it is shown that polynomial interpolation is more efficient than the conventional method of undetermined coefficients for finding coefficients of the scheme. The high-order non-uniform schemes along with boundary closure of up to 14th order thus obtained are shown to be stable on a non-uniform grid with appropriate stretching so that more grid points are clustered near the boundary. The stability and resolution properties of the high-order non-uniform grid schemes are studied and the results of three numerical tests on stability and accuracy properties are also presented.