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In this paper we propose a mesoscale model for polar fluids and numerically investigate its validity by considering well known benchmark cases: the steady and unsteady Poiseuille and the low Reynolds lid-driven cavity flow. Analytical and numerical results are compared with our numerical results and a very good agreement is found. Then we consider not yet investigated high Reynolds lid-driven cavity flow cases, obtaining consistent and interesting results, which encourage to apply the proposed model to more complex cases. [ABSTRACT FROM AUTHOR]

We present a lattice Boltzmann realization of Grad's extended hydrodynamic approach to nonequilibrium flows. This is achieved by using higher-order isotropic lattices coupled with a higher-order regularization procedure. The method is assessed for (low across parallel plates and three-dimensional flows in porous media, showing excellent agreement of the mass flow with analytical and numerical solutions of the Boltzmann equation across the full range of Knudsen numbers, from the hydrodynamic regime to ballistic motion. [ABSTRACT FROM AUTHOR]

In this work, a numerical assessment of the suitability of a Single Relaxation Time (SRT) Lattice Boltzmann Method (LBM) model to simulate axisymmetric gravity currents is carried out. The model results are compared with both experimental data and other numerical models. The particular SRT formulation employed is known to converge, in the limit of low Knudsen number, to the two-layer 2D Shallow Water Equations (SWEs) set with a viscosity term featuring a closed theoretical formulation. Even with the lowest viscosity achievable by the method, its effect is shown to become important in most of the cases analysed, thus posing some serious constraints on possible application of the single relaxation time LBM method to simulate the lock-release generated-type gravity currents analysed here. The comparison with classical numerical models shows that the the viscous effects in the LBM model can be well reproduced employing coefficients derived from the above-mentioned theoretical formulation. [ABSTRACT FROM AUTHOR]