Accurate discretization of advection-diffusion equations

R. Grima, T. J. Newman

    Research output: Contribution to journalArticle

    23 Citations (Scopus)

    Abstract

    We present an exact mathematical transformation which converts a wide class of advection-diffusion equations into a form allowing simple and direct spatial discretization in all dimensions, and thus the construction of accurate and more efficient numerical algorithms. These discretized forms can also be viewed as master equations which provide an alternative mesoscopic interpretation of advection-diffusion processes in terms of diffusion with spatially varying hopping rates.
    Original languageEnglish
    Article number036703
    JournalPhysical Review E: Statistical, Nonlinear, and Soft Matter Physics
    Volume70
    Issue number3
    DOIs
    Publication statusPublished - 16 Sep 2004

    Fingerprint

    Advection-diffusion Equation
    advection
    Discretization
    Advection-diffusion
    Master Equation
    Numerical Algorithms
    Diffusion Process
    Convert
    Efficient Algorithms
    Alternatives
    Form
    Interpretation
    Class

    Cite this

    @article{253197c5bd4243feb896b2e871bd077b,
    title = "Accurate discretization of advection-diffusion equations",
    abstract = "We present an exact mathematical transformation which converts a wide class of advection-diffusion equations into a form allowing simple and direct spatial discretization in all dimensions, and thus the construction of accurate and more efficient numerical algorithms. These discretized forms can also be viewed as master equations which provide an alternative mesoscopic interpretation of advection-diffusion processes in terms of diffusion with spatially varying hopping rates.",
    author = "R. Grima and Newman, {T. J.}",
    year = "2004",
    month = "9",
    day = "16",
    doi = "10.1103/PhysRevE.70.036703",
    language = "English",
    volume = "70",
    journal = "Physical Review E: Statistical, Nonlinear, and Soft Matter Physics",
    issn = "1539-3755",
    publisher = "American Physical Society",
    number = "3",

    }

    Accurate discretization of advection-diffusion equations. / Grima, R.; Newman, T. J.

    In: Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, Vol. 70, No. 3 , 036703, 16.09.2004.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - Accurate discretization of advection-diffusion equations

    AU - Grima, R.

    AU - Newman, T. J.

    PY - 2004/9/16

    Y1 - 2004/9/16

    N2 - We present an exact mathematical transformation which converts a wide class of advection-diffusion equations into a form allowing simple and direct spatial discretization in all dimensions, and thus the construction of accurate and more efficient numerical algorithms. These discretized forms can also be viewed as master equations which provide an alternative mesoscopic interpretation of advection-diffusion processes in terms of diffusion with spatially varying hopping rates.

    AB - We present an exact mathematical transformation which converts a wide class of advection-diffusion equations into a form allowing simple and direct spatial discretization in all dimensions, and thus the construction of accurate and more efficient numerical algorithms. These discretized forms can also be viewed as master equations which provide an alternative mesoscopic interpretation of advection-diffusion processes in terms of diffusion with spatially varying hopping rates.

    UR - http://www.scopus.com/inward/record.url?scp=42749101785&partnerID=8YFLogxK

    U2 - 10.1103/PhysRevE.70.036703

    DO - 10.1103/PhysRevE.70.036703

    M3 - Article

    VL - 70

    JO - Physical Review E: Statistical, Nonlinear, and Soft Matter Physics

    JF - Physical Review E: Statistical, Nonlinear, and Soft Matter Physics

    SN - 1539-3755

    IS - 3

    M1 - 036703

    ER -