Abdoulaye Ouattara | Searcharxiv

arXiv2026

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

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.

physics.flu-dyn↗

arXiv2026

A high-order ghost-point immersed boundary method coupled with auxiliary differential equations for time-domain impedance walls

A ghost-point immersed boundary method is coupled with auxiliary differential equations to impose a locally-reacting impedance condition on a wall that does not conform to a Cartesian grid, in the framework of the linearized Euler equations. The ghost-point reconstruction follows the normal-stencil approach: an elliptical least squares cloud of fluid nodes is used to build a high-order polynomial along the local wall normal, which is then extrapolated onto the ghost points by one-dimensional La grange interpolation. The impedance, modeled as a massspringdamper oscillator, is advanced in time through two auxiliary state variables per ghost point, coupled to the reconstruction at every RungeKutta stage. The method is validated against exact and semi-analytical references on a flat immersed wall, a cylindrical wall reflecting an acoustic pulse, and a cylinder scattering a harmonic monopole. Convergence orders ranging from about three on the curved wall to about four and a half on the flat wall are measured, and a cross-check against an exact harmonic reference shows that a persistent offset observed against a semi-analytical reference is a property of that ref erence rather than of the coupled solver. A spectral stability analysis of the linearized semi-discrete operator further shows that the normal-stencil reconstruction reduces, without eliminating, a known instability that occurs when the immersed wall becomes tangent to the grid.

physics.flu-dyn↗