On the use of the spectral element method for the modeling of fluid–structure interaction problems

This study addresses a fluid–structure interaction problem that models flow in a channel.  Simulations were conducted to investigate the method's effectiveness when applied to real obstacle scenarios, where the obstacle is explicitly represented within the channel.  To tackle the Navier–Stokes equations, we utilized the spectral–Fourier–asymptotic approach, which is a mesh-free method that combines Chebyshev polynomials and Fourier series with the asymptotic method based on power series.

fluid–structure
asymptotic method
spectral mesh-free method
  1. Bonet J., Wood R. D.  Nonlinear continuum mechanics for finite element analysis.  Cambridge University Press (1997).
  2. Burman E., Fernández M. A.  Continuous interior penalty finite element method for the time-dependent Navier–Stokes equations: space discretization and convergence.  Numerische Mathematik.  107, 39–77 (2007).
  3. Drissi M., Mesmoudi S., Mansouri M.  On the use of a high-order spectral method and the geometric progression for the analysis of stationary bifurcation of nonlinear problems.  International Journal of Dynamics and Control.  11, 2633–2643 (2023).
  4. Bertoluzza S., Ismail M., Maury B.  Analysis of the fully discrete fat boundary method.  Numerische Mathematik.  118, 49–77 (2011).
  5. Breuer M., De Nayer G., Münsch M., Gallinger T., Wüchner R.  Fluide structure interaction using a partitioned semi-implicit predictore corrector coupling scheme for the application of large-eddy simulation.  Journal of Fluids and Structures.  29, 107–130 (2012).
  6. Canuto C., Hussaini M. Y., Quarteroni A., Zang T. A.  Spectral methods: fundamentals in single domains.  Springer Science & Business Media (2007).
  7. Drissi M., Mansouri M., Mesmoudi S., Saadouni K.  On the use of a Pseudo-spectral method in the Asymptotic Numerical Method for the resolution of the Ginzburg Landau envelope equation.  Engineering Structures.  262, 114236 (2022).
  8. Drissi M., Mansouri M., Mesmoudi S.  Fluid–structure interaction with the spectral method: application to a cylindrical tube subjected to transverse flow. International Journal of Dynamics and Control.  11, 995–1001 (2023).