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An upwinding cell‐centered method with piecewise constant velocity over covolumes
Author(s) -
Chou So–Hsiang,
Vassilevski Panayot S.
Publication year - 1999
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/(sici)1098-2426(199901)15:1<49::aid-num3>3.0.co;2-g
Subject(s) - piecewise , mathematics , upwind scheme , constant (computer programming) , partition (number theory) , partial differential equation , mathematical analysis , constant coefficients , combinatorics , computer science , discretization , programming language
We analyze as a covolume method an upwinding cell‐centered method derived from a mixed formulation of the convection–diffusion equation. The covolume method uses primal and dual partitions of the problem domain to assign degrees of freedom and is a natural generalization of the well known MAC (Marker and Cell) method. The concentration is cell‐centered (piecewise constant with respect to the primal partition), and the velocity is covolume‐ or co‐cell centered (piecewise constant with respect to the dual partition). Convergence results are demonstrated in the L 2 norm. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 49–62, 1999