TY - JOUR
T1 - Eigensolution analysis of immersed boundary method based on volume penalization
T2 - Applications to high-order schemes
AU - Kou, Jiaqing
AU - Hurtado-de-Mendoza, Aurelio
AU - Joshi, Saumitra
AU - Le Clainche, Soledad
AU - Ferrer, Esteban
N1 - Publisher Copyright:
© 2021 The Author(s)
PY - 2022/1/15
Y1 - 2022/1/15
N2 - 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.
AB - 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.
KW - Eigensolution analysis
KW - Flux reconstruction
KW - High-order methods
KW - Immersed boundary method
KW - Non-modal analysis
KW - Volume penalization
UR - http://www.scopus.com/inward/record.url?scp=85119250717&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2021.110817
DO - 10.1016/j.jcp.2021.110817
M3 - 文章
AN - SCOPUS:85119250717
SN - 0021-9991
VL - 449
JO - Journal of Computational Physics
JF - Journal of Computational Physics
M1 - 110817
ER -