  Embedding geometries in structured grids allows a simple treatment of complex
objects in fluid simulations. Various methods for embedding geometries are
available. The commonly used Brinkman-volume-penalization models geometries as
porous media, and approximates a solid object in the limit of vanishing
porosity. In its simplest form, the momentum equations are augmented by a term
penalizing the fluid velocity, yielding good results in many applications.
However, it induces numerical stiffness, especially if high-pressure gradients
need to be balanced.
  Here, we focus on the effect of the reduced effective volume (commonly called
porosity) of the porous medium. An approach is derived, which allows reducing
the flux through objects to practically zero with little increase of numerical
stiffness. Also, non-slip boundary conditions and adiabatic boundary conditions
are easily constructed. The porosity terms allow keeping the skew symmetry of
the underlying numerical scheme, by which the numerical stability is improved.
Furthermore, very good conservation of mass and energy in the non-penalized
domain can be achieved, for which the boundary smoothing introduces a small
ambiguity in its definition.
  The scheme is tested for acoustic scenarios, for near incompressible and
strongly compressible flows.
