Central moments-based cascaded lattice Boltzmann method for thermal convective flows in three-dimensions

Hajabdollahi, Farzaneh; Premnath, Kannan N.

doi:10.1016/j.ijheatmasstransfer.2017.12.085

Cited by 28 publications

(32 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the following, computational efficiency of two HT models and the DDF thermal model is investigated by numerical experiments on a typical incompressible thermal flow. Natural convection in a square cavity with an aspect ratio equal to unity is investigated by both the DDF model and the hybrid models, which is widely investigated by lattice Boltzmann method [31][32][33]. The Prandtl number is taken equal to 0:71.…”

Section: Hybrid Thermal Lb Modelsmentioning

confidence: 99%

Regularized thermal lattice Boltzmann method for natural convection with large temperature differences

Feng

Guo

Tao

et al. 2018

International Journal of Heat and Mass Transfer

View full text Add to dashboard Cite

A new thermal lattice Boltzmann (LB) method is proposed for the simulation of natural convection with large temperature differences and high Rayleigh number. A regularization procedure is developed on LB equation with a third order expansion of equilibrium distribution functions, in which a temperature term is involved to recover the equation of state for perfect gas. A hybrid approach is presented to couple mass conservation equation, momentum conservation equations and temperature evolution equation. A simple and robust non-conservative form of temperature transport equation is adopted and solved by the finite volume method. A comparison study between classical Double Distribution Function (DDF) model and the hybrid finite volume model with different integration schemes is presented to demonstrate both consistency and accuracy of hybrid models. The proposed model is assessed by simulating several test cases, namely the two-dimensional non-Boussinesq natural convection in a square cavity with large horizontal temperature differences and two unsteady natural convection flows in a tall enclosure at high Rayleigh number. The present method can accurately predict both the steady and unsteady non-Boussinesq convection flows with significant heat transfer. For unsteady natural convection, oscillations with chaotic feature can be well captured in large temperature gradient conditions.

show abstract

Section: Hybrid Thermal Lb Modelsmentioning

confidence: 99%

Regularized thermal lattice Boltzmann method for natural convection with large temperature differences

Feng

Guo

Tao

et al. 2018

International Journal of Heat and Mass Transfer

View full text Add to dashboard Cite

show abstract

“…The construction of the collision step in the LB formulations using central moments based on the peculiar velocity [29,30] naturally maintains the Galilean invariance of the moments independently supported by the lattice and its advantages have been demonstrated for a variety of fluid dynamical problems (see e.g., [31][32][33][34][35][36]). Based on these considerations, we proposed a 2D central moment rectangular LB scheme recently and demonstrated its superior numerical features for simulating flows at higher Reynolds numbers using relatively small grid aspect ratio when compared to the other existing LB methods based on the rectangular lattice [24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Central Moment Lattice Boltzmann Method on a Cuboid Lattice for Anisotropic and Inhomogeneous Flows

Yahia

Schupbach

Premnath

2021

Fluids

Self Cite

View full text Add to dashboard Cite

Lattice Boltzmann (LB) methods are usually developed on cubic lattices that discretize the configuration space using uniform grids. For efficient computations of anisotropic and inhomogeneous flows, it would be beneficial to develop LB algorithms involving the collision-and-stream steps based on orthorhombic cuboid lattices. We present a new 3D central moment LB scheme based on a cuboid D3Q27 lattice. This scheme involves two free parameters representing the ratios of the characteristic particle speeds along the two directions with respect to those in the remaining direction, and these parameters are referred to as the grid aspect ratios. Unlike the existing LB schemes for cuboid lattices, which are based on orthogonalized raw moments, we construct the collision step based on the relaxation of central moments and avoid the orthogonalization of moment basis, which leads to a more robust formulation. Moreover, prior cuboid LB algorithms prescribe the mappings between the distribution functions and raw moments before and after collision by using a moment basis designed to separate the trace of the second order moments (related to bulk viscosity) from its other components (related to shear viscosity), which lead to cumbersome relations for the transformations. By contrast, in our approach, the bulk and shear viscosity effects associated with the viscous stress tensor are naturally segregated only within the collision step and not for such mappings, while the grid aspect ratios are introduced via simpler pre- and post-collision diagonal scaling matrices in the above mappings. These lead to a compact approach, which can be interpreted based on special matrices. It also results in a modular 3D LB scheme on the cuboid lattice, which allows the existing cubic lattice implementations to be readily extended to those based on the more general cuboid lattices. To maintain the isotropy of the viscous stress tensor of the 3D Navier–Stokes equations using the cuboid lattice, corrections for eliminating the truncation errors resulting from the grid anisotropy as well as those from the aliasing effects are derived using a Chapman–Enskog analysis. Such local corrections, which involve the diagonal components of the velocity gradient tensor and are parameterized by two grid aspect ratios, augment the second order moment equilibria in the collision step. We present a numerical study validating the accuracy of our approach for various benchmark problems at different grid aspect ratios. In addition, we show that our 3D cuboid central moment LB method is numerically more robust than its corresponding raw moment formulation. Finally, we demonstrate the effectiveness of the 3D cuboid central moment LB scheme for the simulations of anisotropic and inhomogeneous flows and show significant savings in memory storage and computational cost when used in lieu of that based on the cubic lattice.

show abstract

“…We prescribe the central moment equilibria based on those of the local Maxwellian, by replacing the density with the scalar field φ (see e.g., [54,55,56]). Usually, the third order central moment equilibria then becomeη eq xxy =η eq xyy = 0 and the corresponding raw moment equilibria areη eq xxy = c 2 sφ φu y + φu 2 x u y and η eq xyy = c 2 sφ φu x + φu x u 2 y [54,55,56]. On the other hand, to enable local computation of the vorticity field, our derivation in Secs.…”

Section: Discussionmentioning

confidence: 99%

Local vorticity computation approach in double distribution functions based lattice Boltzmann methods for flow and scalar transport

Hajabdollahi

Premnath

2020

International Journal of Heat and Fluid Flow

Self Cite

View full text Add to dashboard Cite

Computation of vorticity, or the skew-symmetric velocity gradient tensor, in conjunction with the strain rate tensor, plays an important role in fluid mechanics in the flow classification, in vortical structure identification and in the modeling of various complex fluids and flows. For the simulation of flows accompanied by the advection-diffusion transport of a scalar field, double distribution functions (DDF) based lattice Boltzmann (LB) methods, involving a pair of LB schemes are commonly used. We present a new local vorticity computation approach by introducing an intensional anisotropy of the scalar flux in the third order, off-diagonal moment equilibria of the LB scheme for the scalar field, and then combining the second order non-equilibrium components of both the LB methods. As such, any pair of lattice sets in the DDF formulation that can independently support the third order off-diagonal moments would enable local determination of the complete flow kinematics, with the LB methods for the fluid motion and the transport of the passive scalar respectively providing the necessary moment relationships to determine the symmetric and skew-symmetric components of the velocity gradient tensor. Since the resulting formulation is completely local and do not rely on finite difference approximations for velocity derivatives, it is by design naturally suitable for parallel computation. As an illustration of our approach, we formulate a DDF-LB scheme for local vorticity computation using a pair of multiple relaxation times (MRT) based collision approaches on two-dimensional, nine velocity (D2Q9) lattices, where the necessary moment relationships to determine the velocity gradient tensor and the vorticity are established via a Chapman-Enskog analysis. Simulations of various benchmark flows demonstrate good accuracy of the predicted vorticity fields using our approach against available solutions, including numerical results, with a second order convergence. Furthermore, extensions of our formulation for a variety of collision models to enable local vorticity computation are presented.

show abstract

Central moments-based cascaded lattice Boltzmann method for thermal convective flows in three-dimensions

Cited by 28 publications

References 37 publications

Regularized thermal lattice Boltzmann method for natural convection with large temperature differences

Regularized thermal lattice Boltzmann method for natural convection with large temperature differences

Three-Dimensional Central Moment Lattice Boltzmann Method on a Cuboid Lattice for Anisotropic and Inhomogeneous Flows

Local vorticity computation approach in double distribution functions based lattice Boltzmann methods for flow and scalar transport

Contact Info

Product

Resources

About