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A critical evaluation of seven discretization schemes for convection–diffusion equations
Author(s) -
Patel M. K.,
Markatos N. C.,
Cross M.
Publication year - 1985
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.1650050303
Subject(s) - discretization , upwind scheme , mathematics , finite difference , convection–diffusion equation , finite difference method , function (biology) , quadratic equation , diffusion , stability (learning theory) , numerical diffusion , mathematical analysis , geometry , computer science , physics , mechanics , evolutionary biology , machine learning , biology , thermodynamics
A comparative study of seven discretization schemes for the equations describing convection‐diffusion transport phenomena is presented. The (differencing) schemes considered are the conventional central‐ and upwind‐difference schemes, together with the Leonard, 1 Leonard upwind 1 and Leonard super upwind difference 1 schemes. Also tested are the so called locally exact difference scheme 2 and the quadratic‐upstream difference scheme. 3,4 In multidimensional problems errors arise from ‘false‐diffusion’ and function approximations. It is asserted that false diffusion is essentially a multidimensional source of error. No mesh constraints are associated with errors in function approximation and discretization. Hence errors associated with discretization only may be investigated via one‐dimensional problems. Thus, although the above schemes have been tested for one‐ and two‐dimensional flows with sources, only the former are presented here. For 1D flows, the Leonard super upwind difference scheme and the locally exact scheme are shown to be far superior in accuracy to the others at all Peclet numbers and for most source distributions, for the test cases considered. Furthermore, the latter is shown to be considerably cheaper in computational terms than the former. The stability of the schemes and their CPU time requirements are also discussed.