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 [265Jump To The Next Citation Point]. 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.
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