@Article{AAMM-9-4,
author = {Xu, Dan and Xiaogang, Deng and Yaming, Chen and Wang, Guangxue and Yidao, Dong},
title = {Effect of Nonuniform Grids on High-Order Finite Difference Method},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2017},
volume = {9},
number = {4},
pages = {1012--1034},
abstract = {<p style="text-align: justify;">The finite difference (FD) method is popular in the computational fluid dynamics
and widely used in various flow simulations. Most of the FD schemes are
developed on the uniform Cartesian grids; however, the use of nonuniform or curvilinear
grids is inevitable for adapting to the complex configurations and the coordinate
transformation is usually adopted. Therefore, the question that whether the characteristics
of the numerical schemes evaluated on the uniform grids can be preserved on the
nonuniform grids arises, which is seldom discussed. Based on the one-dimensional
wave equation, this paper systematically studies the characteristics of the high-order
FD schemes on nonuniform grids, including the order of accuracy, resolution characteristics
and the numerical stability. Especially, the Fourier analysis involving the
metrics is presented for the first time and the relation between the resolution of numerical
schemes and the stretching ratio of grids is discussed. Analysis shows that for
smooth varying grids, these characteristics can be generally preserved after the coordinate
transformation. Numerical tests also validate our conclusions.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.2016.m1477},
url = {https://global-sci.com/article/73289/effect-of-nonuniform-grids-on-high-order-finite-difference-method}
}