  One route to improved predictive modeling of magnetically confined fusion
reactors is to couple transport solvers with direct numerical simulations (DNS)
of turbulence, rather than with surrogate models. An additional challenge
presented by coupling directly with DNS is that the inherent fluctuations in
the turbulence, which limit the convergence achievable in the transport solver.
In this article, we investigate the performance of one numerical coupling
method in the presence of turbulent fluctuations. To test a particular
numerical coupling method for the transport solver, we use an
autoregressive-moving-average model to efficiently generate stochastic
fluctuations with statistical properties resembling those of a gyrokinetic
simulation. These fluctuations are then added to a simple, solvable problem,
and we examine the behavior of the coupling method. We find that monitoring the
residual as a proxy for the error can be misleading. From a pragmatic point of
view, this study aids us in the full problem of transport coupled to DNS by
predicting the amount of averaging required to reduce the fluctuation error and
obtain a specific level of accuracy.
