Using Newton-GMRES for viscoelastic flow time-steppers

Kinetic theory models exhibit dynamics that depend on a few low-order moments of the underlying conformational distribution function. This dependence is exhibited in a compact spectrum of eigenvalues for the Jacobian matrix associated with the 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. Results are presented for three example problems: (1) the equilibrium behavior of the Doi model with the Onsager excluded volume potential, (2) pressure-driven flow of non-interacting rigid dumbbells in a planar channel, and (3) pressure-driven flow of non-interacting rigid dumbbells through a planar channel with a linear array of equally spaced cylinders.