3.7 Artificial wind method
The fact that classical hydrodynamic equations are Galilean invariant (Lorentz invariant in the
relativistic case) is exploited in the artificial wind (AW) method [265
]. One chooses a reference frame where
the flow through zone interfaces is always supersonic. This reduces the problem of upwinding to a trivial
task (avoiding the need of any spectral decomposition of the flux Jacobians). In case of the global AW
method, the choice of the reference frame is global, whereas in case of the local AW method an appropriate
choice is made at every numerical interface which reduces the numerical diffusion. Explicit expressions for
the velocities of the reference frames (AW velocities) are given to ensure stability and to reduce
diffusion. The resulting expressions for the numerical flux coincide formally with those of the HLL
method. In the differential AW method, AW velocities are chosen as low as possible for each of
the intermediate states between contiguous numerical zones obtained using weighted linear
interpolations.
