Development of Noncentered Wavenumber-Based Optimized Interpolation Schemes with Amplification Control for Overlapping Grids

  • Authors:

  • Damien Desvigne;Olivier Marsden;Christophe Bogey;Christophe Bailly

  • Affiliations:

  • damien.desvigne@ec-lyon.fr and olivier.marsden@ec-lyon.fr and christophe.bogey@ec-lyon.fr and christophe.bailly@ec-lyon.fr;-;-;-

  • Venue:
  • SIAM Journal on Scientific Computing
  • Year:
  • 2010

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Abstract

A noncentered interpolation technique has been constructed to perform simulations using overlapping grids for complex geometries. High-order centered Lagrange polynomial interpolations and interpolations optimized in the Fourier space are first generalized to the noncentered case. These noncentered interpolations either generate significant dispersion errors or strongly amplify high-wavenumber components. Accordingly, a noncentered high-order wavenumber-based optimized interpolation method is developed with the addition of a nonlinear constraint for the control of the amplitude amplification induced by decentering. High-order piecewise polynomial regressions of the obtained interpolation coefficients are performed. The time stability of the method is investigated in the 1-D case when the interpolation method is used in conjunction with explicit high-order differencing, filtering schemes, as well as a 6-step Runge-Kutta time integration algorithm. A criterion is formulated to predict its stability as a function of the filtering strength and the Courant-Friedrichs-Lewy constant. Finally, 1-D convection simulations are presented to illustrate the stability and the accuracy of the developed noncentered interpolations.