  We present a new numerical method for studying the dynamics of quantum fluids
composed of a Bose-Einstein condensate and a cloud of bosonic or fermionic
atoms in a mean-field approximation. It combines an explicit time-marching
algorithm, previously developed for Bose-Einstein condensates in a harmonic or
optical-lattice potential, with a particle-in-cell MonteCarlo approach to the
equation of motion for the one-body Wigner distribution function in the
cold-atom cloud. The method is tested against known analytical results on the
free expansion of a fermion cloud from a cylindrical harmonic trap and is
validated by examining how the expansion of the fermionic cloud is affected by
the simultaneous expansion of a condensate. We then present wholly original
calculations on a condensate and a thermal cloud inside a harmonic well and a
superposed optical lattice, by addressing the free expansion of the two
components and their oscillations under an applied harmonic force. These
results are discussed in the light of relevant theories and experiments.
