  The focusing of acoustic waves is used to study nucleation phenomena in
liquids. At large amplitude, non-linear effects are important so that the
magnitude of pressure or density oscillations is difficult to predict. We
present a calculation of these oscillations in a spherical geometry.
  We show that the main source of non-linearities is the shape of the equation
of state of the liquid, enhanced by the spherical geometry. We also show that
the formation of shocks cannot be ignored beyond a certain oscillation
amplitude. The shock length is estimated by an analytic calculation based on
the characteristics method. In our numerical simulations, we have treated the
shocks with a WENO scheme. We obtain a very good agreement with experimental
measurements which were recently performed in liquid helium. The comparison
between numerical and experimental results allows in particular to calibrate
the vibration of the ceramics used to produce the wave, as a function of the
applied voltage.
