Numerical solution of the Fokker–Planck equation for fiber suspensions: Application to the Folgar–Tucker–Lipscomb model

Numerical Research on the Three-Dimensional Fiber Orientation Distribution in Planar Suspension Flows

“…In the existing literature, the grid resolutions are 39×77 in Advani and Tucker (1990), 40×40 in Férec et al (2008), or were not mentioned in Lin et al (2010). So the calculation is carried on 36×72 grids and the results are listed and compared in Figure 5.…”

“…Furthermore, the finite difference scheme does not guarantee the local flux conservation (Férec et al, 2008;Bay and Tucker, 1992). A finite volume scheme was provided by Bay (1991), Férec et al (2008), Lin et al (2010), Bay and Tucker (1992), but the implementation of the boundary condition was not detailed. In practice, when 0   and 2    , the boundaries are joined together; thus, the spherical symmetrical boundary condition is written as:…”

“…(35), and using Eq. (44), the algebraic equation system can be iteratively solved by the LU decomposition, which has also been denoted as the cyclic tridiagonal-matrix algorithm (C-TDMA) (Férec et al, 2008;Bay and Tucker, 1992).…”

“…The 39×77 grids were used in Advani and Tucker (1990), and the 40×40 grids were used in Férec et al (2008) for the three-dimensional orientation. But the accuracy validation, especially the grid relevance, has not been tested.…”

“…In addition, in the past two decades, the finite volume method has been widely applied in molding process simulation and property analysis (Férec et al, 2008;Pei et al, 2012). In this paper, a numerical scheme based on the finite volume method is presented to solve the three-dimensional orientation distribution function.…”