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An accurate moving grid Eulerian Lagrangian localized adjoint method for solving the one‐dimensional variable‐coefficient ADE
Author(s) -
Younes Anis
Publication year - 2004
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.649
Subject(s) - eulerian path , interpolation (computer graphics) , advection , grid , mathematics , variable (mathematics) , variable coefficient , mathematical analysis , finite volume method , péclet number , range (aeronautics) , convection–diffusion equation , mechanics , geometry , lagrangian , classical mechanics , physics , thermodynamics , motion (physics) , materials science , composite material
An accurate finite‐volume Eulerian Lagrangian localized adjoint method (ELLAM) is presented for solving the one‐dimensional variable coefficients advection dispersion equation that governs transport of solute in porous medium. The method uses a moving grid to define the solution and test functions. Consequently, the need for spatial interpolation, or equivalently numerical integration, which is a major issue in conventional ELLAM formulations, is avoided. After reviewing the one‐dimensional method of ELLAM, we present our strategy and detailed calculations for both saturated and unsaturated porous medium. Numerical results for a constant‐coefficient problem and a variable‐coefficient problem are very close to analytical and fine‐grid solutions, respectively. The strength of the developed method is shown for a large range of CFL and grid Peclet numbers. Copyright 2004 John Wiley & Sons, Ltd.