Logarithmic Mach number of a plane sound wave packet propagating through the Gresho vortex. The upper row shows the unpreconditioned Roe solver, the lower row was computed using the preconditioned Roe solver. The columns show the Mach number at the beginning (left), when the wave is just passing through the vortex (center left), some time after the sound wave has left the domain (center right), and after a full rotation of the vortex (right).
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