  We investigate the numerical performance of the regularized deconvolution
closure introduced recently by the authors. The purpose of the closure is to
furnish constitutive equations for Irwing-Kirkwood-Noll procedure, a well known
method for deriving continuum balance equations from the Newton's equations of
particle dynamics. A version of this procedure used in the paper relies on
spatial averaging developed by Hardy, and independently by Murdoch and Bedeaux.
The constitutive equations for the stress are given as a sum of several
operator terms acting on the mesoscale average density and velocity. Each term
is a "convolution sandwich" containing the deconvolution operator, a
composition or a product operator, and the convolution (averaging) operator.
Deconvolution is constructed using filtered regularization methods from the
theory of ill-posed problems. The purpose of regularization is to ensure
numerical stability. The particular technique used for numerical experiments is
truncated singular value decomposition (SVD). The accuracy of the constitutive
equations depends on several parameters: the choice of the averaging window
function, the value of the mesoscale resolution parameter, scale separation,
the level of truncation of singular values, and the level of spectral filtering
of the averages. We conduct numerical experiments to determine the effect of
each parameter on the accuracy and efficiency of the method. Partial error
estimates are also obtained.
