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On the accuracy of a nonlinear finite volume method for the solution of diffusion problems using different interpolations strategies
Author(s) -
Queiroz L.E.S.,
Souza M.R.A.,
Contreras F.R.L.,
Lyra P.R.M.,
Carvalho D.K.E.
Publication year - 2013
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.3850
Subject(s) - monotonic function , monotone polygon , mathematics , piecewise , finite volume method , nonlinear system , isotropy , interpolation (computer graphics) , piecewise linear function , linear interpolation , mathematical analysis , diffusion , operator (biology) , scheme (mathematics) , numerical analysis , computer science , geometry , physics , polynomial , chemistry , animation , biochemistry , computer graphics (images) , repressor , quantum mechanics , mechanics , transcription factor , gene , thermodynamics
SUMMARY In this paper, we consider a nonlinear finite volume method to solve the steady‐state diffusion equation in nonhomogeneous and non‐isotropic media. The method is nonlinear even if the original problem is linear. In its original form, the scheme is monotone, because the coefficient matrix is monotone under certain assumptions and, as a consequence, whenever the analytic operator demands, it preserves the positivity of numerical solutions. On the other hand, the scheme is unable to reproduce piecewise linear solutions exactly. In order to recover this interesting feature, we use two different interpolation strategies. In this case, even though we are unable to prove monotonicity, we show some numerical evidences that the combined method has an improved behavior, producing second order accurate solutions, even for nonhomogeneous and strongly anisotropic media. Copyright © 2013 John Wiley & Sons, Ltd.