Accuracy of spectral and finite difference schemes in 2D advection problems

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    Abstract

    In this paper we investigate the accuracy of two numerical procedures commonly used to solve 2D advection problems: spectral and finite difference (FD) schemes. These schemes are widely used, simulating, e.g., neutral and plasma flows. FD schemes have long been considered fast, relatively easy to implement, and applicable to complex geometries, but are somewhat inferior in accuracy compared to spectral schemes. Using two study cases at high Reynolds number, the merging of two equally signed Gaussian vortices in a periodic box and dipole interaction with a no-slip wall, we will demonstrate that the accuracy of FD schemes can be significantly improved if one is careful in choosing an appropriate FD scheme that reflects conservation properties of the nonlinear terms and in setting up the grid in accordance with the problem.
    Original languageEnglish
    JournalS I A M Journal on Scientific Computing
    Volume25
    Issue number1
    Pages (from-to)104-126
    ISSN1064-8275
    DOIs
    Publication statusPublished - 2003

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