Ph.D. Dissertation

Brown University, Division of Applied Mathematics, October 2005:

"Numerical Methods for Multi-Scale Modeling of Non-Newtonian Flows"

by VASILEIOS SYMEONIDIS


Abstract: This work presents numerical methods for the simulation of Non-Newtonian fluids in the continuum as well as the mesoscopic level. The former is achieved with Direct Numerical Simulation (DNS) spectral h/p methods, while the latter employs the Dissipative Particle Dynamics (DPD) technique. Physical results are also presented as a motivation for a clear understanding of the underlying numerical approaches.

The macroscopic simulations employ two non-Newtonian models, namely the Reiner-Rivlin (RR) and the viscoelastic FENE-P model.


The mesoscopic simulations assume bead-spring representations of polymer chains and investigate different integrating schemes of the DPD equations and different intra-polymer force combinations.