  Molecular Dynamic (MD) approach is applied to study the converging
cylindrical shock waves in a dense Lennard-Jones (LJ) fluid. MD method is based
on tracking of the atom motions and hence it has an fundamental advantages over
hydrodynamic methods which assumes shocks as a structureless discontinuity and
requires an equation of state. Due to the small thickness of shock fronts in
liquid the two million particles is enough to simulate propagation of a
cylindrical shocks in close detail.
  We investigate stability of converging shocks with different perturbation
modes and its mixture. It was shown that in a case of relatively large initial
ripples the Mach stems are formed. Supersonic jets generated by interaction of
reflected shocks in downstream flow are observed. We also study the
Richtmyer-Meshkov (RM) instability of an interface between two Lennard-Jones
liquids of different mass densities. Surprisingly, mode 3 ripples grow very
slow in comparison with higher mode numbers and growth rate of a higher mode
decay slower.
