  Embedding geometries in structured grids allows a simple treatment of complex
objects in fluid flows. Various methods are available. The commonly used
Brinkman-volume-penalization models geometries as porous media, where in the
limit of vanishing porosity a solid object is approximated. In the simplest
form, the velocity equations are augmented by a term penalizing the fluid
velocity, the body 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 to reduce
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 to keep the skew symmetry of
the underlying numerical scheme, by which the numerical stability is improved.
Furthermore, a very good conservation of mass and energy in the non-penalized
domain can be achieved.
  The scheme is tested for acoustic scenarios, near incompressible and strongly
compressible flows.
