Finite element simulations of viscoplastic flows in the presence of inertia and elastic effects

In this article some computations of inertia flows of elasto-viscoplastic materials down a one-to-four sudden expansion-contraction are performed. The phenomenon is model by the mass usual mass and and momentum balance equations together with an Oldroyd-type viscoelastic equation, modified to accommodate a dependence of both relaxation and retardation time as the viscoplastic viscosity on the material structure level. Such a model is approximated via a three-field Galerkin least-squares method in terms of extra-stress, velocity and pressure fields. According to its design, the compatibility conditions between the extra-stress-velocity and pressure-velocity finite element sub-spaces are bypassed, allowing the method uses equal-order finite element interpolations – more details see [8] and [1]. In the computations, the relevant adimensional elastic and viscous parameters are ranged in order to evaluate their influence on the elasto-viscoplastic fluid dynamics.