The talk Computational study on flows of fluids characterized by non-monotone implicit constitutive relations, by Giordano Tierra, will be held on Monday October 26, 2015 at 9:00 in room K3.
In this talk we present a computational study on unsteady flows of a class of non-Newtonian incompressible fluids characterized by non-monotone constitutive relations relating the symmetric part of the velocity gradient and the deviatoric part of the Cauchy stress. Experimental studies have shown that there are many different substances that exhibit this type of behavior but to our best knowledge, there is no mathematical theory available for the relevant initial and boundary value problems concerning this class of non-monotone constitutive equations.
We propose a novel numerical algorithm based on introducing a nonlinear viscosity function as a new variable, using Finite Differences to discretize the temporal interval, using Finite Elements to discretize the spatial domain and an iterative algorithm to handle the nonlinearities. The achieved numerical results document the stability of the scheme for the range of parameters considered and illustrates the macroscopical non-Newtonian responses that can be captured under these formulations.