  An expression for the stress tensor near an external boundary of a discrete
mechanical system is derived explicitly in terms of the constituents' degrees
of freedom and interaction forces. Starting point is the exact and general
coarse graining formulation presented by Goldhirsch in [I. Goldhirsch, Gran.
Mat., 12(3):239-252, 2010], which is consistent with the continuum equations
everywhere but does not account for boundaries. Our extension accounts for the
boundary interaction forces in a self-consistent way and thus allows the
construction of continuous stress fields that obey the macroscopic conservation
laws even within one coarse-graining width of the boundary.
  The resolution and shape of the coarse-graining function used in the
formulation can be chosen freely, such that both microscopic and macroscopic
effects can be studied. The method does not require temporal averaging and thus
can be used to investigate time-dependent flows as well as static and steady
situations. Finally, the fore-mentioned continuous field can be used to define
'fuzzy' (highly rough) boundaries. Two discrete particle method simulations are
presented in which the novel boundary treatment is exemplified, including a
chute flow over a base with roughness greater than a particle diameter.

Soft Condensed Matter