The computational efficiency of non-linear frequency domain methods

  • Authors:

  • M. S. McMullen;A. Jameson

  • Affiliations:

  • Stanford University, Department of Aeronautics and Astronautics, Durand Building, 496 Lomita Mall, Stanford, CA 94305-4035, United States;Stanford University, Department of Aeronautics and Astronautics, Durand Building, 496 Lomita Mall, Stanford, CA 94305-4035, United States

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

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Abstract

This paper demonstrates efficient solver technologies applied to the non-linear frequency domain (NLFD) method. The basis of the NLFD method is to assume the time period of the solution's oscillation and to transform both the solution and residual using a discrete Fourier transform. An unsteady residual is formed in the frequency domain and iteratively driven to a negligible value. This method is amenable to many of the convergence acceleration techniques used for steady state flows including pseudo-local time stepping, implicit residual averaging, coarse grid viscosity and multigrid. This paper will address the implementation of these techniques such that convergence rates of the modified unsteady solver are equivalent to those of the original steady-state techniques.