Transient 3D free-surface Newtonian and viscoelastic flow as applied to material processing

An adaptive (Lagrangian) boundary element approach is proposed for the general three-dimensional simulation of confined free-surface flow of viscous incompressible fluids. The method is stable as it includes remeshing capabilities of the deforming free surface, and thus can handle large deformations. Newtonian fluids as well as viscoelastic fluids obeying the linear Maxwell constitutive model are considered. Based on the correspondence principle. the viscoelastic integral equations are derived in the time domain, thus avoiding the costly Laplace inversion. Only boundary and not volume integrals are involved. It is shown that the resulting equations, at a given time step, reduce to those corresponding to Stokes flow, but include additional boundary integral contributions from previous flow history. The method is applied to transient extrusion.