Three-dimensional multidomain lattice Boltzmann grid refinement for passive scalar transport

Simulations of passive scalar transport on a three-dimensional (3D) multiresolution grid are presented within the framework of single relaxation time lattice Boltzmann method. The combined modeling of the fluid flow and scalar transport is handled by a double distribution function approach in which the velocity in the fluid flow equation is solved first and then copied to the scalar equation to solve the corresponding scalar quantities. A 3D scaling technique, considering both external forces and scalar source terms, and two-dimensional bicubic interpolation scheme are developed for coupling nonequilibrium velocity and scalar distributions on the interfaces of different resolution grids. The proposed algorithm is validated for three benchmark cases, i.e., the forced convection in a 3D channel, natural convection in a cubical cavity, and turbulent channel flow with heat transfer. Good agreements are found between the present predictions and previous data, which confirms the capability of the proposed method for the computation of passive scalar transport in 3D domains.

Figure 1

(a) D3Q19 and (b) D3Q7 lattice models.

Figure 2

Refinement boundaries between coarse and fine grids.

Figure 3

Calculation processes for a three-level multidomain grid where the number in the bracket represents the order of operations.

Figure 4

Bicubic spatial interpolations from coarse to fine grids.

Figure 5

Schematic diagram of the forced convection in a 3D channel.

Figure 6

Multidomain grid distributions on $xy$ and $yz$ midplanes of the channel.

Figure 7

Velocity and temperature profiles compared with the analytical results for the MG1 grid at $\mathrm{R}{\mathrm{e}}_{\tau }=10$ and $\mathrm{Pr}=0.71$.

Figure 8

Sketch of the natural convection in a cubical cavity.

Figure 9

Multidomain grid distributions on $xy$, $xz$, and $yz$ midplanes of the cubical cavity.

Figure 10

Isotherms on $x=0.5$ and $z=0.5$ midplanes of the cubical cavity for (a) $\mathrm{Ra}={10}^3$, (b) $\mathrm{Ra}={10}^4$, (c) $\mathrm{Ra}={10}^5$, and (d) $\mathrm{Ra}={10}^6$.

Figure 11

Velocity magnitude normalized by the characteristic velocity $u_0=\sqrt{g\beta \left(T_H-T_L\right)H}$ on $x=0.5$ and $z=0.5$ midplanes of the cubical cavity for (a) $\mathrm{Ra}={10}^3$, (b) $\mathrm{Ra}={10}^4$, (c) $\mathrm{Ra}={10}^5$, and (d) $\mathrm{Ra}={10}^6$.

Figure 12

Computational domain for 3D turbulent channel flow with heat transfer.

Figure 13

Mean velocity and temperature profiles compared with DNS results [25].

Figure 14

Reynolds stress component and turbulent heat flux compared with DNS results [25].