The numerical solution of the advection-dispersion equation

A review of some basic principles

Stephen George Wallis

    Research output: Contribution to journalLiterature review

    Abstract

    The simulation of solute transport in rivers is frequently based on numerical models of the Advection-Dispersion Equation. The construction of reliable computational schemes, however, is not necessarily easy. The paper reviews some of the most important issues in this regard, taking the finite volume method as the basis of the simulation, and compares the performance of several types of scheme for a simple case of the transport of a patch of solute along a uniform river. The results illustrate some typical (and well known) deficiencies of explicit schemes and compare the contrasting performance of implicit and semi-Lagrangian versions of the same schemes. It is concluded that the latter have several benefits over the other types of scheme. © Institute of Geophysics, Polish Academy of Sciences 2007.

    Original languageEnglish
    Pages (from-to)85-94
    Number of pages10
    JournalActa Geophysica
    Volume55
    Issue number1
    DOIs
    Publication statusPublished - Mar 2007

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    advection
    finite volume method
    solute transport
    geophysics
    river
    simulation
    solute
    science

    Keywords

    • Advection
    • Finite volume method
    • Numerical modelling
    • Reference frame
    • Solute transport
    • Time marching

    Cite this

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    title = "The numerical solution of the advection-dispersion equation: A review of some basic principles",
    abstract = "The simulation of solute transport in rivers is frequently based on numerical models of the Advection-Dispersion Equation. The construction of reliable computational schemes, however, is not necessarily easy. The paper reviews some of the most important issues in this regard, taking the finite volume method as the basis of the simulation, and compares the performance of several types of scheme for a simple case of the transport of a patch of solute along a uniform river. The results illustrate some typical (and well known) deficiencies of explicit schemes and compare the contrasting performance of implicit and semi-Lagrangian versions of the same schemes. It is concluded that the latter have several benefits over the other types of scheme. {\circledC} Institute of Geophysics, Polish Academy of Sciences 2007.",
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    author = "Wallis, {Stephen George}",
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    The numerical solution of the advection-dispersion equation : A review of some basic principles. / Wallis, Stephen George.

    In: Acta Geophysica, Vol. 55, No. 1, 03.2007, p. 85-94.

    Research output: Contribution to journalLiterature review

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    AB - The simulation of solute transport in rivers is frequently based on numerical models of the Advection-Dispersion Equation. The construction of reliable computational schemes, however, is not necessarily easy. The paper reviews some of the most important issues in this regard, taking the finite volume method as the basis of the simulation, and compares the performance of several types of scheme for a simple case of the transport of a patch of solute along a uniform river. The results illustrate some typical (and well known) deficiencies of explicit schemes and compare the contrasting performance of implicit and semi-Lagrangian versions of the same schemes. It is concluded that the latter have several benefits over the other types of scheme. © Institute of Geophysics, Polish Academy of Sciences 2007.

    KW - Advection

    KW - Finite volume method

    KW - Numerical modelling

    KW - Reference frame

    KW - Solute transport

    KW - Time marching

    U2 - 10.2478/s11600-006-0044-5

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    M3 - Literature review

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    JF - Acta Geophysica

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