Simulating Stochastic Fluid Dynamics

Fluid dynamics, as described in text books, is a deterministic
theory, based on partial differential equations. It has long been
understood that this is not quite right. Fluctuation-dissipation
relations require that any theory that includes dissipation must
be stochastic. In most fluids, stochastic corrections are small,
and encoded in non-analytic long-time tails. Near a phase transition,
however, stochastic effects are large, and lead to critical slowing
down and dynamic scaling. Simulating this behavior numerically is
not trivial. Stochastic fluid dynamics is a stochastic field theory
-- there are UV divergences, and parameters of the theory have
to be renormalized. I described recent progress in performing
simulations of stochastic fluid dynamics, with an emphasis on
creating tools for predicting the dynamics of a heavy ion
collisions near a conjectured QCD critical point.