Analysis of the spectral difference scheme and its implementation in a stream function-vorticity solver

The present study implements the spectral difference scheme in a stream function-vorticity solver and analyzes the convection and diffusion discretization schemes in the wave number space. The solver computes a square lid-driven cavity flow at low Reynolds numbers accurately, but fails at higher Reynolds numbers. An inspection of the discretization procedure in the wave number space reveals distortions which are responsible for the failure of the scheme at high values of Reynolds number. The modified wave numbers of the first derivative at specific solution points display anti-dissipation, indicated by the imaginary component. The second derivative is overly dissipative for a range of wave numbers for the near-interface solution points and at the first point off the wall-boundary it is also anti-dissipative at the highest range of wave numbers. The non-uniformity in the distribution of solution points also induces an imaginary component in the modified wave number for the second derivative, which creates additional dispersive effects. The importance of accuracy in the wave number space is shown by changing the differencing formulas as required, and replacing them by finite difference discretizations. These schemes are appropriately tuned for the chosen grid for better modified wave number properties. The changes allow us to compute high Reynolds number cases successfully.

• Publication year

  2025

• Venue

  Journal of aerospace science and technology

• Publication date

  2025-11-11

• Fields of study

  Not labeled

• Identifiers
  DOI 10.61653/joast.v77i4.2025.1112
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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