  We present simulations of stochastic fluid dynamics in the vicinity of a
critical endpoint belonging to the universality class of the Ising model. This
study is motivated by the challenge of modeling the dynamics of critical
fluctuations near a conjectured critical endpoint in the phase diagram of
Quantum Chromodynamics (QCD). We focus on the interaction of shear modes with a
conserved scalar density, which is known as model H. We show that the observed
dynamical scaling behavior depends on the correlation length and the shear
viscosity of the fluid. As the correlation length is increased or the viscosity
is decreased we observe a cross-over from the dynamical exponent of critical
diffusion, $z\simeq 4$, to the expected scaling exponent of model H, $z\simeq
3$. We use our method to investigate time-dependent correlation function of
non-Gaussian moments $M^n(t)$ of the order parameter. We find that the
relaxation time depends in non-trivial manner on the power $n$.
