An Exponential Time Integrator for the Incompressible Navier--Stokes Equation

Gijs L. Kooij, Mike A. Bochev, Bernard J. Geurts (Corresponding Author)

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    Abstract

    We present an exponential time integration method for the incompressible Navier--Stokes equation. An essential step in our procedure is the treatment of the pressure by applying a divergence-free projection to the momentum equation. The differential-algebraic equation for the discrete velocity and pressure is then reduced to a conventional ordinary differential equation that can be solved with the proposed exponential integrator. A promising feature of exponential time integration is its potential time parallelism within the Paraexp algorithm. We demonstrate that our approach leads to parallel speedup assuming negligible parallel communication.
    Original languageEnglish
    Pages (from-to)B684-B705
    Number of pages22
    JournalSIAM journal on scientific computing
    Volume40
    Issue number3
    DOIs
    Publication statusPublished - 2018

    Keywords

    • Incompressible Navier Stokes equation
    • Block Krylov subspace methods
    • Parallel in time
    • Exponential time integration

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