A finite-volume ELLAM for non-linear flux convection–diffusion problems

In this paper, a modified finite-volume Eulerian–Lagrangian localized adjoint method (FVELLAM) extended for convection–diffusion problems with a non-linear flux function is introduced. Tracking schemes are discussed using viscous Burgers’ equation. It is shown that in order to have smooth results, o...

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Bibliographic Details
Published inInternational journal of non-linear mechanics Vol. 44; no. 2; pp. 130 - 137
Main Authors Fatehi, R., Manzari, M.T., Hannani, S.K.
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.03.2009
Subjects
Convection–diffusion
ELLAM
Finite-volume
Non-linear flux
Two-phase flow in porous media
Non-linear flux
ELLAM
Finite-volume
Convection–diffusion
Two-phase flow in porous media
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Summary:In this paper, a modified finite-volume Eulerian–Lagrangian localized adjoint method (FVELLAM) extended for convection–diffusion problems with a non-linear flux function is introduced. Tracking schemes are discussed using viscous Burgers’ equation. It is shown that in order to have smooth results, only the new time level values should be used in tracking process. Then, the proposed method is employed to study immiscible incompressible two-phase flows in porous media. Various one- and two-dimensional test cases involving internal sources and sinks are solved and accuracy of solution and performance of the method are investigated by comparing the results obtained using FVELLAM with those of fine grid solutions. Finally, it is concluded that although proposed FVELLAM produces satisfactory results even on coarse grids and allows fairly large time-steps, its major advantage is in solving convection-dominated problems in heterogeneous media.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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content type line 23
ISSN:0020-7462
1878-5638
DOI:10.1016/j.ijnonlinmec.2008.10.001