  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.
