Iterated upwind schemes for gas dynamics

  • Authors:

  • Piotr K. Smolarkiewicz;Joanna Szmelter

  • Affiliations:

  • National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307, USA;Loughborough University, Wolfson School of Mechanical and Manufacturing Engineering, Loughborough, Leicestershire LE11 3TU, UK

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2009

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Abstract

A class of high-resolution schemes established in integration of anelastic equations is extended to fully compressible flows, and documented for unsteady (and steady) problems through a span of Mach numbers from zero to supersonic. The schemes stem from iterated upwind technology of the multidimensional positive definite advection transport algorithm (MPDATA). The derived algorithms employ standard and modified forms of the equations of gas dynamics for conservation of mass, momentum and either total or internal energy as well as potential temperature. Numerical examples from elementary wave propagation, through computational aerodynamics benchmarks, to atmospheric small- and large-amplitude acoustics with intricate wave-flow interactions verify the approach for both structured and unstructured meshes, and demonstrate its flexibility and robustness.