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Computation of vorticity in conjunction with the strain rate tensor, plays animportant role in fluid mechanics in vortical structure identification and inthe modeling of various complex fluids. For the simulation of flows accompaniedby the advection-diffusion transport of a scalar field, double distributionfunctions (DDF) based lattice Boltzmann methods (LBMs) are commonly used. Wepresent a new local vorticity computation approach by introducing anintensional anisotropy of the scalar flux in the third order, off-diagonalmoment equilibria of the LB scheme for the scalar field, and then combining thesecond order non-equilibrium components of both the LBMs. As such, any pair oflattice sets in the DDF formulation that can independently support the thirdorder off-diagonal moments would enable local determination of the completeflow kinematics, with the LBMs for the fluid motion and the transport of thepassive scalar respectively providing the necessary moment relationships todetermine the symmetric and skew-symmetric components of the velocity gradienttensor. Since the resulting formulation is completely local and do not rely onfinite difference approximations for velocity derivatives, it is by designnaturally suitable for parallel computation. As an illustration of ourapproach, we formulate a DDF-LB scheme for local vorticity computation using apair of multiple relaxation times (MRT) based collision approaches ontwo-dimensional, nine velocity (D2Q9) lattices, where the necessary momentrelationships to determine the velocity gradient tensor and the vorticity areestablished via a Chapman-Enskog analysis. Simulations of various benchmarkflows demonstrate good accuracy of the predicted vorticity fields, with asecond order convergence. Furthermore, extensions of our formulation for avariety of collision models to enable local vorticity computation arepresented.

Local Vorticity Computation in Double Distribution Functions based Lattice Boltzmann Methods for Flow and Scalar Transport