A High-Order Immersed Boundary Technique for Computational Aeroacoustics
Résumé
Finite difference methods are widely employed for numerical simulation in aeroacoustics, a domain in which high-order, low-dispersive and low-dissipative methods are widespread. However, finite differences are restricted to Cartesian grids. When solids of arbitrary shape are present in the simulation, it is possible to use immersed boundary methods (IBM) to avoid boundary-fitted grids. The order of IBM methods is often restricted to 2, even if several high-order IBM methods have been presented in the literature for aeroacoustics. However, we have found these methods to be rather unstable. In this work we seek for a stable, high-order immersed boundary method, for use in the Navier Stokes equations. The technique treats the immersed boundaries as a sharp interface by enforcing boundary conditions through ghost points. These are computed using characteristics and extrapolation along the normal direction to the interface. The method is tested on convective and diffusive problems, and has been applied to benchmark problems for the linearized Euler equations. High orders of convergence could be observed on model problems, with little change in time-step size, without filtering playing an essential role. \\[10pt] References : \item Seo, J. H., \& Mittal, R. ``A high-order immersed boundary method for acoustic wave scattering and low-Mach number flow-induced sound in complex geometries''. Journal of computational physics, 230(4), (2011): 1000-1019. \item Lu, J., et al. ``Inverse Lax–Wendroff procedure for numerical boundary conditions of convection– diffusion equations''. Journal of Computational Physics 317 (2016): 276-300. \item Wiegmann, A., \& K. P. Bube. ``The explicit-jump immersed interface method: finite difference methods for PDEs with piecewise smooth solutions''. SIAM Journal on Numerical Analysis 37.3 (2000): 827-862. \item Lu, J., et al. ``An inverse Lax-Wendroff procedure for hyperbolic conservation laws with changing wind direction on the boundary''. Journal of Computational Physics 426 (2021): 109940. \end{itemize}
Domaines
Acoustique [physics.class-ph]Origine | Fichiers éditeurs autorisés sur une archive ouverte |
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