A super-grid-scale model for simulating compressible flow on unbounded domains

  • Authors:

  • Tim Colonius;Hongyu Ran

  • Affiliations:

  • Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California;Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2002

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Abstract

A new buffer region (absorbing layer, sponge layer, fringe region) technique for computing compressible flows on unbounded domains is proposed. We exploit the connection between coordinate-mapping from bounded to unbounded domains and filtering of the equations of motion in Fourier space in order to develop a model to damp flow disturbances (advective and acoustic) that propagate outside an arbitrarily defined near field. This effectively simulates a free-space boundary condition. Damping the solution in the far field is accomplished in a simple and effective way by applying a filter (similar to that used in large-eddy simulation) on a mesh in Fourier space, followed by a secondary filtering of the equations on the physical grid and implementation of a model for the unresolved scales. The final form of the buffer region is given in real space, independent of any discretization of the equations. Here we use a dealiased, Fourier spectral collocation method to demonstrate the efficacy of the buffer region for several model problems: acoustic wave propagation, convection of a finite-amplitude vortex, and a viscous starting jet in two dimensions. The results compare favorably to previous nonreflecting and absorbing boundary conditions.