Hybrid recursive regularized lattice Boltzmann simulation of humid air with application to meteorological flows

An extended version of the hybrid recursive regularized lattice-Boltzmann model which incorporates external force is developed to simulate humid air flows with phase change mechanisms under the Boussinesq approximation. Mass and momentum conservation equations are solved by a regularized lattice Boltzmann approach well suited for high Reynolds number flows, whereas the energy and humidity related equations are solved by a finite volume approach. Two options are investigated to account for cloud formation in atmospheric flow simulations. The first option considers a single conservation equation for total water and an appropriate invariant variable of temperature. In the other approach, liquid and vapor are considered via two separated equations, and phase transition is accounted for via a relaxation procedure. The obtained models are then systematically validated on four well-established benchmark problems including a double diffusive Rayleigh Bénard convection of humid air, two- and three-dimensional thermal moist rising bubble under convective atmospheric environment, as well as a shallow cumulus convection in the framework of large-eddy simulation.

Figure 1

The flowchart of LB method with condensation model (2eq) (potential temperature $\theta$, vapor humidity $q_v$, and cloud liquid specific humidity $q_l$).

Figure 2

Temperature contours obtained by the LB method (2eq model) for $\text{Ra}={10}^4$ (top), and $\text{Ra}={10}^5$ (bottom).

Figure 3

Contours of water fraction obtained by the LB method (2eq model) on $\text{Ra}={10}^4$ (top), $\text{Ra}={10}^5$ (bottom).

Figure 4

Profile of velocity along midline of domain (top: velocity $u$ along $y$; bottom: velocity $v$ along $x$). The double diffusive Rayleigh Bénard convection with $\text{Ra}={10}^4$ and ${10}^5$ are presented on $50\times 50$ and $100\times 100$ grid resolutions by the proposed LB method.

Figure 5

Comparison of velocities ($u,v$) along midlines of domain with different nondimensional relaxation time $\tau$ at $\mathrm{Ra}={10}^4$ on $50\times 50$ grids.

Figure 6

Local Nusselt number at the hot wall. The double diffusive Rayleigh Bénard convection with $\mathrm{Ra}={10}^4$ and ${10}^5$ is presented on $50\times 50$ and $100\times 100$ grid resolutions by the proposed LB method.

Figure 7

Left panels: Streamlines and contours of liquid humidity field at 2 min (top) and 3 min (bottom) obtained by the present LB method with 1eq model and 2eq models. In each panel, the left part is obtained by 2eq model while the right part is from 1eq model. Right panels: Streamlines and contours of liquid humidity field at 5 min (top) and 7 min (bottom) obtained by the present LB method with 1eq model and 2eq model. In each figure, the left part is obtained by 2eq model while the right part is from 1eq model.

Figure 8

Contours of vorticity and liquid humidity field obtained by 1eq model (top) and 2eq model (bottom) at 7 min with excitation of instability on resolution of 5 m in domain of [1100 m, 2500 m] $\times$ [800 m, 1800 m].

Figure 9

Contours of vorticity and liquid humidity field obtained by 1eq model (top) and 2eq model (bottom) at 10 min with excitation of instability on resolution of 5 m in domain of [1100 m, 2500 m] $\times$ [800 m, 1800 m].

Figure 10

Setup of three-dimensional geometry and subdomains for simulation of 3D rising moist thermal bubble.

Figure 11

Contours of liquid humidity field (left) and vapor humidity field (right) at 2, 4, and 6 min (top to bottom)as obtained by the present LB method with 2eq condensation model.

Figure 12

Contours of vertical velocity (left) and $x$ component of vorticity (right) at 2, 4, and 6 min (top to bottom) as obtained by the present LB method with 2eq model and grid refinement.

Figure 13

Profile of liquid humidity and vertical velocity along vertical middle line at 2, 4, 6 min. The symbols represent benchmark solution in Ref. [61].

Figure 14

Mean profiles of vapor water (top, left), liquid water (top, right), velocity (bottom, left), and potential temperature (bottom, right) obtained in the convective cumulus convection case. The reference data in symbols are results at 6 h from [37].

Figure 15

Isosurface of liquid water (top) and temperature (bottom) at 1.5 h for shallow cumulus convection.