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On the use of large time steps with ELLAM for transport with kinetic reactions over heterogeneous domains
Author(s) -
Fahs Marwan,
Younes Anis,
Delay Frederick
Publication year - 2009
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.11727
Subject(s) - eulerian path , advection , dispersion (optics) , nonlinear system , variable (mathematics) , tracking (education) , space time , kinetic energy , mathematics , lagrangian , reaction rate , statistical physics , spacetime , mechanics , mathematical optimization , mathematical analysis , physics , classical mechanics , thermodynamics , chemistry , optics , psychology , pedagogy , biochemistry , quantum mechanics , catalysis
An Eulerian Lagrangian localized adjoint method (ELLAM) is considered for the resolution of advection‐dominated transport problems in porous media. Contrary to standard Eulerian methods, ELLAM can use large time steps because the advection term is approximated accurately without any CFL restriction. However, it is shown in this article that special care must be taken for the approximation of the dispersive and reactive terms when large time steps are used over heterogeneous domains. An alternative procedure is proposed. It is based on an equivalent dispersion coefficient or an equivalent reaction rate when different zones are encountered during the tracking. Numerical experiments are performed with variable dispersion or variable reaction rates over space (including nonlinearity). When classical ELLAM require numerous time steps to handle heterogeneity, the alternative procedure is shown to perform with the same accuracy in a single time step. © 2009 American Institute of Chemical Engineers AIChE J, 2009