Simulations of stochastic fluid dynamics near a critical point in the phase diagram

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 4, to the expected scaling exponent of model H, z 3. We use our method to investigate time-dependent correlation function of non-Gaussian moments Mⁿ (t) of the order parameter. We find that the relaxation time depends in non-trivial manner on the power n.