Short note: On the spectral properties of shock-capturing schemes

  • Authors:

  • Sergio Pirozzoli

  • Affiliations:

  • Universití degli Studi di Roma 'La Sapienza', Dipartimento di Meccanica e Aeronautica, Via Eudossiana 18, 00184 Roma, Italy

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2006

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Abstract

In this short note we analyze the performance of nonlinear, shock-capturing schemes in wavenumber space. For this purpose we propose a new representation for the approximate dispersion relation which accounts to leading order for nonlinear effects. Several examples are presented, which confirm that the present theory yields an improved qualitative representation of the true solution behavior compared to conventional representations. The theory can provide useful guidance for the choice of the most cost-effective schemes for specific applications, and may constitute a basis for the development of optimized ones.