  We present a new and efficient phase-field solver for viscoelastic fluids
with moving contact line based on a dual-resolution strategy. The interface
between two immiscible fluids is tracked by using the Cahn-Hilliard phase-field
model, and the viscoelasticity incorporated into the phase-field framework. The
main challenge of this approach is to have enough resolution at the interface
to approach the sharp-interface methods. The method presented here addresses
this problem by solving the phase field variable on a mesh twice as fine as
that used for the velocities, pressure, and polymer-stress constitutive
equations. The method is based on second-order finite differences for the
discretization of the fully coupled Navier-Stokes, polymeric constitutive and
Cahn-Hilliard equations, and it is implemented in a 2D pencil-like domain
decomposition to benefit from existing highly-scalable parallel algorithms. A
FFT-based solver is used for the Helmholtz and Poisson equations with different
global sizes. The splitting method proposed by previous authors is used to
impose the dynamic contact angle boundary conditions in the case of large
density and viscosity ratios. The implementation is validated against
experimental data and previous numerical studies in 2D and 3D. The results
indicate that the dual-resolution approach produces nearly identical results
while saving computational time for both Newtonian and viscoelastic flows in
3D.
