  High Peclet number, turbulent convection is a classic system with a large
timescale separation between flow speeds and the thermal relaxation time. In
this paper, we present a method of fast-forwarding through the long thermal
relaxation of convective simulations, and we test the validity of this method.
This accelerated evolution (AE) method involves measuring the dynamics of
convection early in a simulation and using its characteristics to adjust the
mean thermodynamic profile within the domain towards its evolved state. We
study Rayleigh-B\'enard convection as a test case for AE. Evolved flow
properties of AE solutions are measured to be within a few percent of solutions
which are reached through standard evolution (SE) over a full thermal
timescale. At the highest values of the Rayleigh number at which we compare SE
and AE, we find that AE solutions require roughly an order of magnitude fewer
computing hours to evolve than SE solutions.
