**2. Numerical Method**

The flow of compressible viscous fluids can mathematically be described by the Navier–Stokes equations governing the conservation of mass, momentum, and energy. In this section, we describe the compressible Navier–Stokes equation with the Brinkman penalization method to model solid obstacles as proposed in [9]. We apply this penalization in the frame of the Discontinuous Galerkin (DG) method and introduce this method also briefly in this section. The additional source terms introduced by the penalization increase the stiffness of the scheme considerably, and the last part of this section discusses how this can be overcome by an implicit-explicit time integration scheme.
