Thesis Summary:

A viscoplastic fluid is one that drains under a sufficiently high pressure gradient. Examples of such fluids are sludges that are produced in mining, ketchup and toothpaste. The classic Darcy-dominated linear EDP problem, which relates a velocity field to a pressure field, is modified to describe the behavior of a viscoplastic fluid. The EDP proposed by Protopapas et al. We introduce and study a mixed primal type problem where the problem stiffness matrix comes from a nonlinear operator, then an approximate scheme is shown to establish existence of solution of the continuous problem. A numerical method is proposed to solve the associated nonlinear problem. Some illustrative numerical experiments are shown. A boundary problem is introduced and a heuristic method is presented to find its solution, which shows that it is not robust. The problem is reformulated using variational inequalities, the equivalence of this new problem is tested and a numerical method is introduced to find its solution. It gives rise to a system of non-linear inequalities. A yield parameter of a viscoplastic fluid is designed and constructed and such an experiment is modeled. Numerical results are compared with exact measurements.