Stephen Montgomery-Smith, David Jack and Douglas E. Smith, The Fast Exact Closure for Jeffery's Equation with Diffusion.
Journal of Non-Newtonian Fluid Mechanics, Volume 166, Issues 7-8, April 2011, Pages 343-353 .
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 diffusion is absent it exactly solves Jeffery's equation. Numerical examples are provided with both Folgar-Tucker (1984) diffusion and the recent anisotropic rotary diffusion of Phelps and Tucker (2009). Computations demonstrate that the FEC exhibits improved accuracy with computational speeds equivalent to or better than existing closure approximations.
(pdf, actual article.)
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