TY - JOUR
T1 - Numerical Solution of Partial Differential Equations in Arbitrary Shaped Domains Using Cartesian Cut-Stencil Finite Difference Method. Part I: Concepts and Fundamentals
AU - Esmaeilzadeh , M.
AU - Barron , R.M.
AU - Balachandar , R.
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 881
EP - 907
PY - 2020
DA - 2020/06
SN - 13
DO - http://doi.org/10.4208/nmtma.OA-2019-0143
UR - https://global-sci.org/intro/article_detail/nmtma/16958.html
KW - Cartesian cut-stencils, finite difference method, irregular domains, convection-diffusion equation, local truncation error.
AB - <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>