  There has been an increasing interest in developing efficient immersed
boundary method (IBM) based on Cartesian grids, recently in the context of
high-order methods. IBM based on volume penalization is a robust and easy to
implement method to avoid body-fitted meshes and has been recently adapted to
high order discretisations (Kou et al., 2021). This work proposes an
improvement over the classic penalty formulation for flux reconstruction high
order solvers. We include a selective frequency damping (SFD) approach
(Aakervik et al., 2006) acting only inside solid body defined through the
immersed boundary masking, to damp spurious oscillations. An encapsulated
formulation for the SFD method is implemented, which can be used as a wrapper
around an existing time-stepping code. The numerical properties have been
studied through eigensolution analysis based on the advection equation. These
studies not only show the advantages of using the SFD method as an alternative
of the traditional volume penalization, but also show the favorable properties
of combining both approaches. This new approach is then applied to the
Navier-Stokes equation to simulate steady flow past an airfoil and unsteady
flow past a circular cylinder. The advantages of the SFD method in providing
improved accuracy are reported.
