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.