(492g) Using Newton-Gmres For Viscoelastic Flow Time-Steppers
AIChE Annual Meeting
2007
2007 Annual Meeting
Computing and Systems Technology Division
Numerical Methods for Molecular and Mesoscopic Systems
Wednesday, November 7, 2007 - 5:30pm to 5:50pm
Kinetic theory models for polymeric liquids exhibit macroscopic dynamics that depend on a few, low-order moments of the underlying conformational distribution function. This dependence is generally exploited to write closed constitutive models for the stress tensor by assuming that the remaining higher-order moments quickly become functionals of these few, lower-order, slow moments. This occurs over timescales that are short compared to the timescale associated with the evolution of the slow moments. Except for very simple kinetic theory models, this process entails the use of closure approximations for higher moments; and these closure approximations can have a significant, qualitative impact on model predictions. We present a method that avoids these approximations by exploiting the compact spectrum of eigenvalues exhibited by the linearized dynamical system. We take advantage of this spectrum of eigenvalues through Newton-GMRES iterations to enable dynamic viscoelastic simulators (time-steppers) to obtain stationary states and perform stability/bifurcation analysis.