  A new time relaxation model with iterative modified Lavrentiev regularization
method is studied. The aim of the relaxation term is to drive the unresolved
fluctuations in a computational simulation to zero exponentially faster by an
appropriate and often problem-dependent choice of its time relaxation
parameter; together with iterative modified Lavrentiev regularization, the
model will give a better approximation through de-convolution with fewer steps
to compute. The goal of this paper herein is to understand how this time
relaxation term acts to truncate solution scales and to use this understanding
to give some helpful insight into parameter selection.
