Accurate discretization of advection-diffusion equations

R. Grima, T. J. Newman

    Research output: Contribution to journalArticlepeer-review

    25 Citations (Scopus)


    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
    Issue number3
    Publication statusPublished - 16 Sept 2004


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