  In this short note, we discuss the use of arithmetic averages for the
evaluation of viscous coefficients such as temperature and velocity components
at a face as required in a cell-centered finite-volume viscous discretization
on unstructured grids, and show that second-order accuracy can be achieved even
when the arithmetic average is not linearly-exact second-order reconstruction
at a face center (e.g., the face center is not located exactly halfway between
two adjacent cell centroids) as typical in unstructured grids. Unlike inviscid
discretizations, where the solution has to be reconstructed in a linearly exact
manner to the face center for second-order accuracy, the viscous discretization
does not require the linear exactness for computing viscous coefficients at a
face. There are two requirements for second-order accuracy, and the arithmetic
average satisfies both of them. Second-order accuracy is numerically
demonstrated for a simple one-dimensional nonlinear diffusion problem and for a
three-dimensional viscous problem based on methods of manufactured solutions.
