@Article{CiCP-18-3,
author = {},
title = {Effect of Geometric Conservation Law on Improving Spatial Accuracy for Finite Difference Schemes on Two-Dimensional Nonsmooth Grids},
journal = {Communications in Computational Physics},
year = {2015},
volume = {18},
number = {3},
pages = {673--706},
abstract = {<p style="text-align: justify;">It is well known that grid discontinuities have significant impact on the performance
of finite difference schemes (FDSs). The geometric conservation law (GCL) is
very important for FDSs on reducing numerical oscillations and ensuring free-stream
preservation in curvilinear coordinate system. It is not quite clear how GCL works in
finite difference method and how GCL errors affect spatial discretization errors especially
in nonsmooth grids. In this paper, a method is developed to analyze the impact
of grid discontinuities on the GCL errors and spatial discretization errors. A violation
of GCL causes GCL errors which depends on grid smoothness, grid metrics method
and finite difference operators. As a result, there are more source terms in spatial discretization
errors. The analysis shows that the spatial discretization accuracy on non-sufficiently
smooth grids is determined by the discontinuity order of grids and can
approach one higher order by following GCL. For sufficiently smooth grids, the spatial
discretization accuracy is determined by the order of FDSs and FDSs satisfying the
GCL can obtain smaller spatial discretization errors. Numerical tests have been done
by the second-order and fourth-order FDSs to verify the theoretical results.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.250614.060215a},
url = {https://global-sci.com/article/80337/effect-of-geometric-conservation-law-on-improving-spatial-accuracy-for-finite-difference-schemes-on-two-dimensional-nonsmooth-grids}
}