  We develop semiclassical methods for describing real-time dynamics of
dissipative Bose-Hubbard systems in a strongly interacting regime, which can be
realized in experiments with ultracold gases. Specifically, we present two
kinds of SU(3) truncated Wigner approximation (TWA) for solving an effective
Lindblad master equation of the systems. The first one employs the discrete TWA
for finite levels or spin systems and is based on a classical equation of
motion in which the onsite dissipation term, as well as the onsite interaction
term, is linearized in the phase space variables. The other approach utilizes a
stochastic Langevin equation, including decoherence effects in terms of
nonlinear drift force and stochastic force terms, in which the initial
conditions of trajectories are weighted with a quasiprobability distribution
for a typical initial quantum state. We apply these methods to the systems with
two-body losses and compare their results with the exact numerical solutions
for a small system. We show that the former approach can simulate correctly
longer-time dynamics than the latter one. We also calculate the time evolution
for a large size setup that is comparable to experiments. We numerically
demonstrate that the discrete TWA approach is able to qualitatively capture the
continuous quantum Zeno effect on dynamics subjected to a gradual change of the
ratio between the hopping amplitude and the onsite interaction across the
superfluid-Mott insulator crossover, which has been observed experimentally.
