A semi-lagrangian strategy to predict the fiber orientation in the steady flows of reinforced thermoplastics Original Research Article

The equations governing the fiber orientation of a short fiber reinforced thermoplastic are hyperbolic (non-linear transport-type equation). The most accurate technique for the treatment of these equations is the method of characteristics. In the present paper, a “semi-lagrangian” strategy is proposed, which reduces drastically the CPU time associated with the integration of the orientation equation. This strategy combines an integration by characteristics into each element of a standard finite element mesh, with a polynomial interpolation of the gradient of deformation tensor on the mesh skeleton. Moreover when a linear approximation of the velocity field is assumed in each element, then the integration by characteristics can be carried out with explicit formulae.