  We perform large-scale real-time simulations of a bubble wall sweeping
through an out-of-equilibrium plasma. The scenario we have in mind is the
electroweak phase transition, which may be first order in extensions of the
Standard Model, and produce such bubbles. The process may be responsible for
baryogenesis and can generate a background of primordial cosmological
gravitational waves. We study thermodynamic features of the plasma near the
advancing wall, the generation of Chern-Simons number/Higgs winding number and
consider the potential for CP-violation at the wall generating a baryon
asymmetry. A number of technical details necessary for a proper numerical
implementation are developed.
