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A brief note on upwind collocation
Author(s) -
Dougherty D. E.,
Pinder G. F.
Publication year - 1983
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.1650030309
Subject(s) - upwind scheme , collocation (remote sensing) , mathematics , advection , diffusion , mathematical analysis , hermite polynomials , convection–diffusion equation , collocation method , geometry , physics , computer science , discretization , differential equation , ordinary differential equation , machine learning , thermodynamics
Upwind collocation on Hermite cubics is compared to orthogonal collocation with respect to effective diffusion. The one‐dimensional constant coefficient advection‐diffusion equation is employed to this end. The effective diffusion coefficient is determined exactly and is found to be dependent on the nodal solution values. The effective diffusion coefficients of three other upwinding schemes are also presented. Upwind collocation is found to have an effective diffusion coefficient like other upwinding schemes plus an extra term which may enhance or reduce the non‐advective flux, depending on the problem solution and point location within the domain.