High-order immersed boundary method for subsonic aeroacoustics and compressible Navier-Stokes equationsHigh-order immersed boundary method for subsonic aeroacoustics and compressible Navier-Stokes equations
Abstract
In computational fluid dynamics, the immersed boundary method is a classical technique to account for complex geometries when Cartesian grids are used, as is the case in finite difference methods. The present paper presents a new discrete ghost point method, which is one of the different immersed boundary methods available, for solving problems in acoustics and aeroacoustics with the linearized Euler equations or the compressible Navier-Stokes equations. This method is based on high-order schemes and a ghost point method. The flow field values at the ghost points are determined in two steps. A least-squares interpolation is first used to reconstruct the flow on a stencil of points located on the normal to the immersed boundary. Then, a 4th order Lagrangian extrapolation based on the normal stencil points adjacent to the boundary point is used to impose the boundary conditions at the immersed boundary by reconstructing the field values at the ghost points. This approach is verified and validated for the acoustical problem of a pressure pulse impinging on a cylinder. The approach is also validated for compressible flow past a circular cylinder at several Reynolds numbers.
Related
- Unification of The Navier-Stokes Equation for Fluid Mechanics and Aeroacoustics
- Simultaneous energy and entropy stability of volume-penalisation immersed-boundary methods for the compressible Navier--Stokes equations
- A ghost-cell immersed boundary method for the shallow water equations on Cartesian grids: mass conservation and wetting and drying over variable topography
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- Guaranteed wave-speed bounds for the compressible Euler equations with a composite equation of state
BibTeX
@misc{ouattara2026highorder,
title = {{High-order immersed boundary method for subsonic aeroacoustics and compressible Navier-Stokes equationsHigh-order immersed boundary method for subsonic aeroacoustics and compressible Navier-Stokes equations}},
author = {Abdoulaye Ouattara and David Marx and Christian Prax and Véronique Fortunée and Manuel Diaz and Peter Jordan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24729},
eprint = {2609.24729},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24729},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - High-order immersed boundary method for subsonic aeroacoustics and compressible Navier-Stokes equationsHigh-order immersed boundary method for subsonic aeroacoustics and compressible Navier-Stokes equations
AU - Abdoulaye Ouattara
AU - David Marx
AU - Christian Prax
AU - Véronique Fortunée
AU - Manuel Diaz
AU - Peter Jordan
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24729
UR - https://arxiv.org/abs/2609.24729
AB - In computational fluid dynamics, the immersed boundary method is a classical technique to account for complex geometries when Cartesian grids are used, as is the case in finite difference methods. The present paper presents a new discrete ghost point method, which is one of the different immersed boundary methods available, for solving problems in acoustics and aeroacoustics with the linearized Euler equations or the compressible Navier-Stokes equations. This method is based on high-order schemes and a ghost point method. The flow field values at the ghost points are determined in two steps. A least-squares interpolation is first used to reconstruct the flow on a stencil of points located on the normal to the immersed boundary. Then, a 4th order Lagrangian extrapolation based on the normal stencil points adjacent to the boundary point is used to impose the boundary conditions at the immersed boundary by reconstructing the field values at the ghost points. This approach is verified and validated for the acoustical problem of a pressure pulse impinging on a cylinder. The approach is also validated for compressible flow past a circular cylinder at several Reynolds numbers.
ER -