Eigensolution analysis of immersed boundary method based on volume penalization: Applications to high-order schemes

Jiaqing Kou, Aurelio Hurtado-de-Mendoza, Saumitra Joshi, Soledad Le Clainche, Esteban Ferrer

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

This paper presents eigensolution and non-modal analyses for immersed boundary methods (IBMs) based on volume penalization for the linear advection equation. This approach is used to analyze the behavior of flux reconstruction (FR) discretization, including the influence of polynomial order and penalization parameter on numerical errors and stability. Through a semi-discrete analysis, we find that the inclusion of IBM adds additional dissipation without changing significantly the dispersion of the original numerical discretization. This agrees with the physical intuition that in this type of approach, the solid wall is modelled as a porous medium with vanishing viscosity. From a stability point of view, the variation of penalty parameter can be analyzed based on a fully-discrete analysis, which leads to practical guidelines on the selection of penalization parameter. Numerical experiments indicate that the penalization term needs to be increased to damp oscillations inside the solid (i.e. porous region), which leads to undesirable time step restrictions. As an alternative, we propose to include a second-order term in the solid for the no-slip wall boundary condition. Results show that by adding a second-order term we improve the overall accuracy with relaxed time step restriction. This indicates that the optimal value of the penalization parameter and the second-order damping can be carefully chosen to obtain a more accurate scheme. Finally, the approximated relationship between these two parameters is obtained and used as a guideline to select the optimum penalty terms in a Navier-Stokes solver, to simulate flow past a cylinder.

Original languageEnglish
Article number110817
JournalJournal of Computational Physics
Volume449
DOIs
StatePublished - 15 Jan 2022
Externally publishedYes

Keywords

  • Eigensolution analysis
  • Flux reconstruction
  • High-order methods
  • Immersed boundary method
  • Non-modal analysis
  • Volume penalization

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