@Article{JCM-42-1305,
author = {Kong , WangHong , ZhenyingYuan , Guangwei and Sheng , Zhiqiang},
title = {Monotonicity Corrections for Nine-Point Scheme of Diffusion Equations},
journal = {Journal of Computational Mathematics},
year = {2024},
volume = {42},
number = {5},
pages = {1305--1327},
abstract = {<p style="text-align: justify;">In this paper, we present a nonlinear correction technique to modify the nine-point
scheme proposed in [SIAM J. Sci. Comput., 30:3 (2008), 1341-1361] such that the resulted
scheme preserves the positivity. We first express the flux by the cell-centered unknowns
and edge unknowns based on the stencil of the nine-point scheme. Then, we use a nonlinear
combination technique to get a monotone scheme. In order to obtain a cell-centered finite
volume scheme, we need to use the cell-centered unknowns to locally approximate the
auxiliary unknowns. We present a new method to approximate the auxiliary unknowns
by using the idea of an improved multi-points flux approximation. The numerical results
show that the new proposed scheme is robust, can handle some distorted grids that some
existing finite volume schemes could not handle, and has higher numerical accuracy than
some existing positivity-preserving finite volume schemes.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2303-m2022-0139},
url = {http://global-sci.org/intro/article_detail/jcm/23279.html}
}