A multi-domain Fourier pseudospectral time-domain method for the linearized Euler equations

  • Authors:

  • Maarten Hornikx;Wim De Roeck;Wim Desmet

  • Affiliations:

  • Building Physics and Services, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands;Mechanical Engineering, K.U. Leuven, Celestijnenlaan 300 B, B-3001 Leuven, Belgium;Mechanical Engineering, K.U. Leuven, Celestijnenlaan 300 B, B-3001 Leuven, Belgium

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2012

Quantified Score

Hi-index 31.45

Visualization

Abstract

The Fourier pseudospectral time-domain (F-PSTD) method is computationally one of the most cost-efficient methods for solving the linearized Euler equations for wave propagation through a medium with smoothly varying spatial inhomogeneities in the presence of rigid boundaries. As the method utilizes an equidistant discretization, local fine scale effects of geometry or medium inhomogeneities require a refinement of the whole grid which significantly reduces the computational efficiency. For this reason, a multi-domain F-PSTD methodology is presented with a coarse grid covering the complete domain and fine grids acting as a subgrid resolution of the coarse grid near local fine scale effects. Data transfer between coarse and fine grids takes place utilizing spectral interpolation with super-Gaussian window functions to impose spatial periodicity. Local time stepping is employed without intermediate interpolation. The errors introduced by the window functions and the multi-domain implementation are quantified and compared to errors related to the initial conditions and from the time iteration scheme. It is concluded that the multi-domain methodology does not introduce significant errors compared to the single-domain method. Examples of scattering from small scale density scatters, sound reflecting from a slitted rigid object and sound propagation through a jet are accurately modelled by the proposed methodology. For problems that can be solved by F-PSTD, the presented methodology can lead to a significant gain in computational efficiency.