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

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

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    Abstract

    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 other situations: specifically diffusion problems with rough initial data; and general advection-diffusion problems with different physical time scales governing the system evolution
    Original languageEnglish
    Pages (from-to)2018-2054
    Number of pages37
    JournalSIAM Journal on Scientific Computing
    Volume30
    Issue number4
    DOIs
    Publication statusPublished - 2008

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    Keywords

    • Time-stepping
    • Adaptivity
    • Convection-diffusion

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