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2008, Volume 1, Issue 4: 573-590. Doi: 10.3934/krm.2008.1.573
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Oscillatory behavior of Asymptotic-Preserving splitting methods for a linear model of diffusive relaxation

  • 1.

    Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, Wisconsin 53706

  • 2.

    Computational Physics Group (CCS-2) and Center for Nonlinear Studies (T-CNLS), Mail Stop B258, Los Alamos National Laboratory, Los Alamos, New Mexico 87544

Received:  August 31, 2008
Revised:  August 31, 2008
Published:  October 2008
Abstract Related Papers Cited by
    Abstract
  • The occurrence of oscillations in a well-known asymptotic preserving (AP) numerical scheme is investigated in the context of a linear model of diffusive relaxation, known as the $P_1$ equations. The scheme is derived with operator splitting methods that separate the $P_1$ system into slow and fast dynamics. A careful analysis of the scheme shows that binary oscillations can occur as a result of a black-red diffusion stencil and that dispersive-type oscillations may occur when there is too little numerical dissipation. The latter conclusion is based on comparison with a modified form of the $P_1$ system. Numerical fixes are also introduced to remove the oscillatory behavior.
    Mathematics Subject Classification: 65M06, 82C70, 82C80.

    Citation:
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