Direct numerical simulations bf statistically-stationary homogeneous i
sotropic turbulence require an artificial input of energy via a forcin
g scheme: Previous forcing methods based on a stochastic addition of e
nergy have resulted in a poor representation of the energy-containing
range of the energy spectrum function and significant temporal fluctua
tions of energy and other large-scale quantities. In this work a deter
ministic forcing scheme for direct numerical simulation is developed w
hich 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 sh
own to be robust and computationally efficient, resulting in velocity
and scalar fields which quickly reach stationarity. It also has the si
gnificant advantages over stochastic forcing methods of not introducin
g additional statistical variability into the computations and allowin
g more physically realistic large-scale motions. (C) 1998 Elsevier Sci
ence Ltd. All rights reserved.