An adaptive central-upwind weighted essentially non-oscillatory scheme

  • Authors:

  • X. Y. Hu;Q. Wang;N. A. Adams

  • Affiliations:

  • Lehrstuhl für Aerodynamik, Technische Universität München, 85748 Garching, Germany;Lehrstuhl für Aerodynamik, Technische Universität München, 85748 Garching, Germany and Chinese Academy of Aerospace Aerodynamics, 100074 Beijing, China;Lehrstuhl für Aerodynamik, Technische Universität München, 85748 Garching, Germany

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2010

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Abstract

In this work, an adaptive central-upwind 6th-order weighted essentially non-oscillatory (WENO) scheme is developed. The scheme adapts between central and upwind schemes smoothly by a new weighting relation based on blending the smoothness indicators of the optimal higher order stencil and the lower order upwind stencils. The scheme achieves 6th-order accuracy in smooth regions of the solution by introducing a new reference smoothness indicator. A number of numerical examples suggest that the present scheme, while preserving the good shock-capturing properties of the classical WENO schemes, achieves very small numerical dissipation.