Finite element approximation for single-phase multicomponent flows

With the objective of performing computational simulations of mixture problems, this work employed a mechanical modeling of single-phase incompressible multicomponent flows able to deal with geometric and material non-linearities. This model is based on conservative laws of mass and momentum in continuum mechanics, assuming the mixture as a superposition of a number of continuous media, each one with a variable volume fraction field. Using appropriate hypothesis, the model was formulated as a set of non-linear partial differential equations and associated boundary conditions. This set was approximated by a stabilized finite element method, based on a Galerkin/least-squares scheme, in order to circumvent Babuška-Brezzi condition and to generate stable approximations even in highly advective situations. Some preliminary numerical results have been obtained for non-Newtonian axial injections in backward facing step incompressible flows.