3 research outputs found
Energy-stable linear schemes for polymer-solvent phase field models
We present new linear energy-stable numerical schemes for numerical
simulation of complex polymer-solvent mixtures. The mathematical model proposed
by Zhou, Zhang and E (Physical Review E 73, 2006) consists of the Cahn-Hilliard
equation which describes dynamics of the interface that separates polymer and
solvent and the Oldroyd-B equations for the hydrodynamics of polymeric
mixtures. The model is thermodynamically consistent and dissipates free energy.
Our main goal in this paper is to derive numerical schemes for the
polymer-solvent mixture model that are energy dissipative and efficient in
time. To this end we will propose several problem-suited time discretizations
yielding linear schemes and discuss their properties
Global existence of weak solutions to viscoelastic phase separation: Part II Degenerate Case
The aim of this paper is to prove global in time existence of weak solutions
for a viscoelastic phase separation. We consider the case with singular
potentials and degenerate mobilities. Our model couples the diffusive interface
model with the Peterlin-Navier-Stokes equations for viscoelastic fluids. To
obtain the global in time existence of weak solutions we consider appropriate
approximations by solutions of the viscoelastic phase separation with a regular
potential and build on the corresponding energy and entropy estimates.Comment: 29 pages, 28 figure
Global existence of weak solutions to viscoelastic phase separation: Part I Regular Case
We prove the existence of weak solutions to a viscoelastic phase separation
problem in two space dimensions. The mathematical model consists of a
Cahn-Hilliard-type equation for two-phase flows and the Peterlin-Navier-Stokes
equations for viscoelastic fluids. We focus on the case of a polynomial-like
potential and suitably bounded coefficient functions. Using the
Lagrange-Galerkin finite element method complex behavior of solution for
spinodal decomposition including transient polymeric network structures is
demonstrated.Comment: 48 pages,11 figure