Dynamics of shear flow of a non-Newtonian fluid
Journal of Computational Physics
Analysis of new phenomena in shear flow of non-Newtonian fluids
SIAM Journal on Applied Mathematics
High-resolution conservative algorithms for advection in incompressible flow
SIAM Journal on Numerical Analysis
Wave propagation algorithms for multidimensional hyperbolic systems
Journal of Computational Physics
SIAM Journal on Scientific Computing
A wave propagation method for hyperbolic systems on the sphere
Journal of Computational Physics
A stable and convergent scheme for viscoelastic flow in contraction channels
Journal of Computational Physics
SIAM Journal on Scientific Computing
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We study the Doi model for suspensions of rod-like molecules. The Doi model couples a microscopic Fokker-Planck type equation (Smoluchowski equation) to the macroscopic Stokes equation. The Smoluchowski equation describes the evolution of the distribution of the rod orientations; it comes as a drift diffusion equation on the sphere at every point in physical space.For sufficiently high macroscopic shear rates (high Deborah numbers), the solution of the coupled system develops internal layers in the macroscopic strain rate (the spurt phenomenon).In the high Deborah numbers regime, the drift term in the Smoluchowski equation is dominant. We thus introduce a finite-volume type discretization of the microscopic Smoluchowski equation which is motivated by transport-dominated PDEs.We carry out direct numerical simulations of the spurt phenomenon both in the dilute and concentrated regimes. Below the isotropic-nematic transition, the solution structure is identical to the one described by purely macroscopic models (JSO model). For higher concentrations, we observe the formation of microstructure coming from a position-dependent tumbling rate. We also investigate the 2-d stability of the spurted solution.