Benchmarking solutions of the Folgar–Tucker-Equation and its reduction to a linear problem for non-linear closure forms

The Folger–Tucker-Equation (FTE) arises from a modification of the Jeffery equation and describes orientation elongated particles in flow by means tensor A. Though FTE represents most widespread commercially used relaxation for A simulations injection molding short-fiber reinforced fluids, analytical solutions formulation applied industry are hardly investigated. Previous work focused on solution underlying (modified) Jeffery’s its integration to rather than direct FTE. present paper firstly introduces lemma that reduces nonlinear formulations linear problems. Its is numerically computational less intensive one original Secondly, this presents benchmarking validate simulation algorithms. Thirdly, closer look at two dimensional enables deeper understanding mathematical behavior popular differential equation. influence rotational components velocity field process analyzed. Finally an extension three case discussed shortly.