Generalized lattice Boltzmann equation with forcing term for computation of wall-bounded turbulent flows

Abstract

In this paper, we present a framework based on the generalized lattice Boltzmann equation (GLBE) 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 (SGS) turbulence effects are represented by the standard Smagorinsky eddy viscosity model, which is modified by using the van Driest wall-damping function to account for reduction of turbulent length scales near walls. In order to be able to simulate a wider class of problems, we introduce forcing terms, which can represent the effects of general nonuniform forms of forces, 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 nonequilibrium moments of the GLBE to include such forcing terms, which comprise a generalization of those presented in a recent work [Yu, Comput. Fluids 35, 957 (2006)]. Variable resolutions are introduced into this extended GLBE framework through a conservative multiblock approach. The approach, whose optimized implementation is also discussed, is assessed for two canonical flow problems bounded by walls, viz., fully developed turbulent channel flow at a shear or friction Reynolds number (Re) of 183.6 based on the channel half-width and three-dimensional (3D) shear-driven flows in a cubical cavity at a 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. The GLBE approach also exhibited markedly better stability characteristics and avoided spurious near-wall turbulent fluctuations on coarser grids when compared with the single-relaxation-time (SRT)-based approach. Moreover, its implementation showed excellent parallel scalability on a large parallel cluster with over a thousand processors.

A comparative study of direct‐forcing immersed boundary‐lattice Boltzmann methods for stationary complex boundaries

“…In addition, for the generalization of the split-forcing IB-LBM, we consider not only Guo et al's split-forcing LBE [35] but also Cheng and Li's split-forcing LBE [38]. The latter enables us to extend our direct-forcing IB-LBM based on split-forcing LBE with single-relaxation time (SRT) to generalized split-forcing LBE with multi-relaxation time (MRT) [39], which is important for the broad applications of the IB-LBM, especially for high-Reynolds flows, because the LBE with MRT can attain better stability than the LBE with SRT. In Section 2.2, we account for explicit and implicit diffuse and sharp interface schemes to be assessed in this study.…”

Incorporating forcing terms in cascaded lattice Boltzmann approach by method of central moments

“…By carefully separating the relaxation times of hydrodynamic and non-hydrodynamic moments, it has been shown that the MRT-LBM significantly improves the numerical stability [17,18] and better physical representation in certain problems such as kinetic layers near boundaries [19], when compared with the SRT-LBM. Such MRT models have recently been shown to reproduce challenging fluid mechanics problems such as complex turbulent flows with good quantitative accuracy [20,21]. An important and natural simplification of the MRT model is the two-relaxation-time (TRT) model, in which the moments of even and odd orders are relaxed at different rates [22].…”

Steady state convergence acceleration of the generalized lattice Boltzmann equation with forcing term through preconditioning

“…The change in distribution function due to collisions as a relaxation process and external forces is represented by ̟, and following Premnath et al [46] it can written as…”

“…density ρ and momentum − → j , are as follows [37]: The components of the source terms in moment space are functions of external force − → F and velocity fields − → u , and are given as follows [46]:…”

“…The MRT-LBE has also been extended for multiphase flows [38,39,40,41,42], and, more recently, for magnetohydrodynamic problems [43], with superior stability characteristics. It has also been used for LES of a class of turbulent flows [44,45,46]. It is known that for a given grid resolution and Reynolds number, the standard LBM based on the SRT model becomes less stable as Ma is lowered due to the relaxation time becoming smaller [47,26].…”