Modelling and simulations of non-Newtonian fluid flows

by 1971- Lee, Young-Ju

iii We observe that various rate-type non-Newtonian constitutive equations can be recast into the well-known symmetric Riccati equations. From the careful study on the Riccati form of various models, some robust and stable discretizations of the rate-type models are constructed. Discrete analogue of energy estimates have been derived and confirm the stability of our new schemes. As a consequence of discrete energy estimates, a global existence and uniqueness of an approximate solution is established regardless of the size of the “Weissenberg number”. We discuss how to solve the resulting discrete problem based upon the preconditioned