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 -

A new finite difference (FD) method, referred to as "Cartesian cut-stencil FD", is introduced to obtain the numerical solution of partial differential equations on any arbitrary irregular shaped domain. The 2nd-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.