  Lattice Boltzmann model for viscoelastic flow simulation is proposed; elastic
effects are taken into account in the framework of Maxwell model. The following
three examples are studied using the proposed approach: a transverse velocity
autocorrelation function for free evolving system with random initial
velocities, a boundary-driven propagating shear waves, and a resonant
enhancement of oscillations in a periodically driven fluid in a capillary. The
measured shear wave dispersion relation is found to be in a good agreement with
the theoretical one derived for the Navier-Stokes equation with the Maxwell
viscoelastic term.
