@Article{NMTMA-13-4,
author = {R.M., Barron and M., Esmaeilzadeh and R., Balachandar and R.M., Barron and R., Balachandar},
title = {Numerical Solution of Partial Differential Equations in Arbitrary Shaped Domains Using Cartesian Cut-Stencil Finite Difference Method. Part I: Concepts and Fundamentals},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2020},
volume = {13},
number = {4},
pages = {881--907},
abstract = {<p style="text-align: justify;">A new finite difference (FD) method, referred to as &quot;Cartesian cut-stencil
FD&quot;, is introduced to obtain the numerical solution of partial differential equations
on any arbitrary irregular shaped domain. The 2<sup>nd</sup>-order accurate two-dimensional
Cartesian cut-stencil FD method utilizes a 5-point stencil and relies on the construction of a unique mapping of each physical stencil, rather than a cell, in any arbitrary
domain to a generic uniform computational stencil. The treatment of boundary conditions and quantification of the solution accuracy using the local truncation error
are discussed. Numerical solutions of the steady convection-diffusion equation on
sample complex domains have been obtained and the results have been compared
to exact solutions for manufactured partial differential equations (PDEs) and other
numerical solutions.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2019-0143},
url = {https://global-sci.com/article/90372/numerical-solution-of-partial-differential-equations-in-arbitrary-shaped-domains-using-cartesian-cut-stencil-finite-difference-method-part-i-concepts-and-fundamentals}
}