Adaptive time-stepping for incompressible flow part I: Scalar advection-diffusion

Philip M. Gresho, David F. Griffiths, David J. Silvester

    Research output: Contribution to journalArticlepeer-review


    Even the simplest advection-diffusion problems can exhibit multiple time scales. This means that robust variable step time integrators are a prerequisite if such problems are to be efficiently solved computationally. The performance of the second order trapezoid rule using an explicit Adams-Bashforth method for error control is assessed in this work. This combination is particularly well suited to long time integration of advection-dominated problems. Herein it is shown that a stabilized implementation of the trapezoid rule leads to a very effective integrator in othersituations: specifically diffusion problems with rough initial data; and general advection-diffusion problems with different physical time scales governing the system evolution. © 2008 Society for Industrial and Applied Mathematics.
    Original languageEnglish
    Pages (from-to)2018-2054
    Number of pages36
    JournalSIAM Journal on Scientific Computing
    Issue number4
    Publication statusPublished - 2007


    • Adaptivity
    • Convection-diffusion
    • Time-stepping


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