Numerical Solution of Partial Differential Equations in Arbitrary Shaped Domains Using Cartesian Cut-Stencil Finite Difference Method. Part I: Concepts and Fundamentals
Year: 2020
Author: R.M. Barron, M. Esmaeilzadeh, R. Balachandar, R.M. Barron, R. Balachandar
Numerical Mathematics: Theory, Methods and Applications, Vol. 13 (2020), Iss. 4 : pp. 881–907
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2019-0143
Numerical Mathematics: Theory, Methods and Applications, Vol. 13 (2020), Iss. 4 : pp. 881–907
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: Cartesian cut-stencils finite difference method irregular domains convection-diffusion equation local truncation error.