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High‐order approximation of 2D convection‐diffusion equation on hexagonal grids
Author(s) -
Karaa Samir
Publication year - 2006
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20149
Subject(s) - stencil , mathematics , scheme (mathematics) , convection–diffusion equation , hexagonal crystal system , partial differential equation , diffusion , hexagonal tiling , mathematical analysis , central differencing scheme , grid , finite difference , finite difference method , order (exchange) , differential equation , diffusion equation , point (geometry) , numerical solution of the convection–diffusion equation , finite difference coefficient , geometry , finite element method , physics , thermodynamics , chemistry , computational science , finance , service (business) , economy , mixed finite element method , economics , crystallography
We derive a fourth‐order finite difference scheme for the two‐dimensional convection‐diffusion equation on an hexagonal grid. The difference scheme is defined on a single regular hexagon of size h over a seven‐point stencil. Numerical experiments are conducted to verify the high accuracy of the derived scheme, and to compare it with the standard second‐order central difference scheme. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2006