Numerical Solution of Partial Differential Equations in Arbitrary Shaped Domains Using Cartesian Cut-Stencil Finite Difference Method. Part II: Higher-Order Schemes
Year: 2022
Author: R.M. Barron, M. Esmaeilzadeh, R.M. Barron
Numerical Mathematics: Theory, Methods and Applications, Vol. 15 (2022), Iss. 3 : pp. 819–850
Abstract
Compact higher-order (HO) schemes for a new finite difference method, referred to as the Cartesian cut-stencil FD method, for the numerical solution of the convection-diffusion equation in complex shaped domains have been addressed in this paper. The Cartesian cut-stencil FD method, which employs 1-D quadratic transformation functions to map a non-uniform (uncut or cut) physical stencil to a uniform computational stencil, can be combined with compact HO Padé-Hermitian formulations to produce HO cut-stencil schemes. The modified partial differential equation technique is used to develop formulas for the local truncation error for the cut-stencil HO formulations. The effect of various HO approximations for Neumann boundary conditions on the solution accuracy and global order of convergence are discussed. The numerical results for second-order and compact HO formulations of the Cartesian cut-stencil FD method have been compared for test problems using the method of manufactured solutions.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2021-0129
Numerical Mathematics: Theory, Methods and Applications, Vol. 15 (2022), Iss. 3 : pp. 819–850
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 32
Keywords: Cartesian cut-stencil finite difference method compact higher-order formulation irregular domain Neumann boundary conditions local truncation error.