On the Eulerian-Lagrangian Formulation of Balance Equations in Porous Media

Jacob Bear, Shaul Sorek, Viacheslav Borisov

    Research output: Contribution to journalArticlepeer-review

    5 Scopus citations


    The article presents a general approach to modeling the transport of extensive quantities in the case of flow of multiple multicomponent fluid phases in a deformable porous medium domain under nonisothermal conditions. The models are written in a modified Eulerian-Lagrangian formulation. In this modified formulation, the material derivatives are written in terms of modified velocities. These are the velocities at which the various phase and component variables propagate in the domain, along their respective characteristic curves. It is shown that these velocities depend on the heterogeneity of various solid matrix and fluid properties. The advantage of this formulation, with respect to the usually employed Eulerian one, is that numerical dispersion, associated with the advective fluxes of extensive quantities, are eliminated. The methodology presented in the article shows how the Eulerian-Lagrangian formulation is written in terms of the relatively small number of primary variables of a transport problem.

    Original languageEnglish
    Pages (from-to)505-530
    Number of pages26
    JournalNumerical Methods for Partial Differential Equations
    Issue number5
    StatePublished - 1 Jan 1997


    • Eulerian-Lagrangian formulation
    • Modeling
    • Porous medium
    • Primary variables
    • Reduced velocities
    • Transport phenomena

    ASJC Scopus subject areas

    • Analysis
    • Numerical Analysis
    • Computational Mathematics
    • Applied Mathematics


    Dive into the research topics of 'On the Eulerian-Lagrangian Formulation of Balance Equations in Porous Media'. Together they form a unique fingerprint.

    Cite this