Modified Fem for Fibre-Fluid Interactions

Summary

The motion of flexible fibres suspended in an incompressible flow is of interest to researchers in various fields and in particular in textile manufacturing. This work deals with the coupled problem of a single fibre moving in the flow field. An elegant way to describe their interactions might well be to embed the fibre’s motion within a meshless flow concept using the ideas of the partition of unity method (PUM). The construction of PUM spaces that depend on the flow test spaces permits the adoption of the flow resolution and a simplification of the external forces acting on the fibre. The stability and accuracy of the PUM depend on the quality of the fibre cover: a filter algorithm is described that improves this quality. Simulations are presented to demonstrate the applicability of this method but the fact that the approximation spaces need to be modified at each time step can lead to a considerable increase in computational time.