Short Note: A limiter for PPM that preserves accuracy at smooth extrema

  • Authors:

  • Phillip Colella;Michael D. Sekora

  • Affiliations:

  • Applied Numerical Algorithms Group, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA;Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08540, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2008

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Abstract

We present a new limiter for the PPM method of Colella and Woodward [P. Colella, P.R. Woodward, The Piecewise Parabolic Method (PPM) for gas-dynamical simulations, Journal of Computational Physics 54 (1984) 174-201] that preserves accuracy at smooth extrema. It is based on constraining the interpolated values at extrema (and only at extrema) using non-linear combinations of various difference approximations of the second derivatives. Otherwise, we use a standard geometric limiter to preserve monotonicity away from extrema. This leads to a method that has the same accuracy for smooth initial data as the underlying PPM method without limiting, while providing sharp, non-oscillatory representations of discontinuities.