Lattice Boltzmann method for viscoelastic fluids.

A lattice Boltzmann model for viscoelastic flow simulation is proposed. Elastic effects are taken into account within the framework of a Maxwell model. To test the approach, we estimate the transverse velocity autocorrelation function for a freely evolving system, and find clear manifestations of shear at large frequencies. We then characterize boundary-driven shear waves, and the resonant enhancement of shear oscillations in a periodically driven fluid confined within a capillary. The measured shear-wave dispersion relation is compared to that obtained from the Navier-Stokes equation with a Maxwell viscoelastic term, and good agreement is obtained.