Lattice Boltzmann method simulation of rotating channel flows: Improved modeling of diffusion and advection terms

Abstract

This work presents an extensive analysis of the lattice Boltzmann method for solving rotating fluid flows inside channel-like geometries, a topic relevant to many scientific and engineering fields. The present research investigates the role of the collision operator, equilibrium and source term formulations, the number of discrete velocities in three-dimensional cubic lattices, and boundary schemes applied to this problem class. Here, it is considered the two-relaxation-time (TRT) collision operator with both equilibrium and source terms represented on the Hermite expansion formalism. Denoting by H(n) the n-order Hermite orthonormal basis, the TRT modeling of the isothermal Navier–Stokes equations expands the symmetric and anti-symmetric components of equilibrium up to H(2) and H(1), respectively, and at H(1) for the external source term, featuring the Coriolis force. This study proposes higher-order expansions of equilibrium and source terms to improve the accuracy of diffusion and advection in rotating fluids. Diffusion modeling is improved by including an H(3) correction to the source term expansion to remedy artifacts from the Coriolis force discretization. Advection modeling is improved by including an H(4) correction to the H(2) expansion of the symmetric equilibrium in the D3Q19 lattice to retrieve an isotropy comparable to the D3Q27. These improvements are derived based on the exact analytical solution of the TRT equation at the discrete level and the steady Chapman–Enskog fourth-order expansion of the TRT solution, respectively, applied to two well-known benchmarks in this problem class: the Poiseuille–Ekman