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

49 pages, 30 figures, To appear in Physical Review E

References in corpus (10)

• Numerical Simulations of Particulate Suspensions via a Discretized Boltzmann Equation Part I. Theoretical Foundation
• Three-Dimensional Multi-Relaxation Time (MRT) Lattice-Boltzmann Models for Multiphase Flow
• Fluctuating lattice Boltzmann
• Role of the H theorem in lattice Boltzmann hydrodynamic simulations
• Entropic lattice Boltzmann methods
• Comparison of Spectral Method and Lattice Boltzmann Simulations of Two-Dimensional Hydrodynamics
• Consistent Lattice Boltzmann Method
• Large-eddy simulation of the flow in a lid-driven cubical cavity
• Kinetic Theory of Turbulence Modeling: Smallness Parameter, Scaling and Microscopic Derivation of Smagorinsky Model
• Turbulent channel flow simulations using a coarse-grained extension of the Lattice Boltzmann method

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• Incorporating Forcing Terms in Cascaded Lattice-Boltzmann Approach by Method of Central Moments
• Dynamic Subgrid Scale Modeling of Turbulent Flows using Lattice-Boltzmann Method
• Steady State Convergence Acceleration of the Generalized Lattice Boltzmann Equation with Forcing Term through Preconditioning
• Inertial Frame Independent Forcing for Discrete Velocity Boltzmann Equation: Implications for Filtered Turbulence Simulation