  Computation of vorticity in conjunction with the strain rate tensor, plays an
important role in fluid mechanics in vortical structure identification and in
the modeling of various complex fluids. For the simulation of flows accompanied
by the advection-diffusion transport of a scalar field, double distribution
functions (DDF) based lattice Boltzmann methods (LBMs) are commonly used. We
present a new local vorticity computation approach by introducing an
intensional anisotropy of the scalar flux in the third order, off-diagonal
moment equilibria of the LB scheme for the scalar field, and then combining the
second order non-equilibrium components of both the LBMs. As such, any pair of
lattice sets in the DDF formulation that can independently support the third
order off-diagonal moments would enable local determination of the complete
flow kinematics, with the LBMs for the fluid motion and the transport of the
passive scalar respectively providing the necessary moment relationships to
determine the symmetric and skew-symmetric components of the velocity gradient
tensor. Since the resulting formulation is completely local and do not rely on
finite difference approximations for velocity derivatives, it is by design
naturally suitable for parallel computation. As an illustration of our
approach, we formulate a DDF-LB scheme for local vorticity computation using a
pair of multiple relaxation times (MRT) based collision approaches on
two-dimensional, nine velocity (D2Q9) lattices, where the necessary moment
relationships to determine the velocity gradient tensor and the vorticity are
established via a Chapman-Enskog analysis. Simulations of various benchmark
flows demonstrate good accuracy of the predicted vorticity fields, with a
second order convergence. Furthermore, extensions of our formulation for a
variety of collision models to enable local vorticity computation are
presented.
