Abstract
Direct numerical simulations of statistically-stationary homogeneous isotropic turbulence require an artificial input of energy via a forcing scheme. Previous forcing methods based on a stochastic addition of energy have resulted in a poor representation of the energy-containing range of the energy spectrum function and significant temporal fluctuations of energy and other large-scale quantities. In this work a deterministic forcing scheme for direct numerical simulation is developed which uses wave number-dependent linear amplification of the lower-wave number modes, relaxing them over time toward a model energy spectrum function, which accurately represents grid turbulence. The scheme is shown to be robust and computationally efficient, resulting in velocity and scalar fields which quickly reach stationarity. It also has the significant advantages over stochastic forcing methods of not introducing additional statistical variability into the computations and allowing more physically realistic large-scale motions.
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