Generalized Lattice-Boltzmann Equation with Forcing Term for Computation of Wall-Bounded Turbulent Flows

TL;DR

This paper introduces a generalized lattice-Boltzmann framework with forcing terms for simulating wall-bounded turbulent flows, improving stability and accuracy in near-wall turbulence modeling.

Contribution

The paper develops a flexible GLBE approach with multiple relaxation times and forcing terms, enhancing stability and fidelity in turbulent flow simulations near walls.

Findings

Accurate reproduction of near-wall turbulence statistics.

Enhanced numerical stability on coarser grids.

Successful application to turbulent channel and cavity flows.

Abstract

We present a framework based on the generalized lattice-Boltzmann equation using multiple relaxation times with forcing term for eddy capturing simulation of wall bounded turbulent flows. Due to its flexibility in using disparate relaxation times, the GLBE is well suited to maintaining numerical stability on coarser grids and in obtaining improved solution fidelity of near-wall turbulent fluctuations. The subgrid scale turbulence effects are represented by the standard Smagorinsky eddy-viscosity model, which is modified by using the van Driest wall-damping function for near wall effects. For simulation of a wider class of problems, we introduce general forcing terms in the natural moment space of the GLBE. Expressions for the strain rate tensor used in the SGS model are derived in terms of the non-equilibrium moments of the GLBE to include such forcing terms. Variable resolutions are introduced into this extended GLBE framework through a conservative multiblock approach. The approach is assessed for two canonical flow problems bounded by walls, viz., fully-developed turbulent channel flow at a shear or friction Reynolds number ($\mathrm{Re}$) of 183.6 based on the channel half-width and three-dimensional (3D) shear-driven flows in a cubical cavity at a $\mathrm{Re}$ of 12,000 based on the side length of the cavity. Comparisons of detailed computed near-wall turbulent flow structure, given in terms of various turbulence statistics, with available data, including those from direct numerical simulations (DNS) and experiments showed good agreement, with marked improvement in numerical stability characteristics.