  Jeffery's equation with diffusion is widely used to predict the motion of
concentrated fiber suspensions in flows with low Reynold's numbers.
Unfortunately, the evaluation of the fiber orientation distribution can require
excessive computation, which is often avoided by solving the related second
order moment tensor equation. This approach requires a `closure' that
approximates the distribution function's fourth order moment tensor from its
second order moment tensor. This paper presents the Fast Exact Closure (FEC)
which uses conversion tensors to obtain a pair of related ordinary differential
equations; avoiding approximations of the higher order moment tensors
altogether. The FEC is exact in that when there are no fiber interactions, it
exactly solves Jeffery's equation. Numerical examples for dense fiber
suspensions are provided with both a Folgar-Tucker (1984) diffusion term and
the recent anisotropic rotary diffusion term proposed by Phelps and Tucker
(2009). Computations demonstrate that the FEC exhibits improved accuracy with
computational speeds equivalent to or better than existing closure
approximations.
