A semi-lagrangian strategy to predict the fiber orientation in the steady flows of reinforced thermoplastics
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.
fiber orientation method of characteristics transport equation upwinding methods