Atmospheric convection on one GPU: a conservative finite-volume scalar transport on the link mass fluxes of the lattice Boltzmann method, compared with large-eddy simulation

We add dry and moist atmospheric convection to FluidX3D, an open-source GPU lattice Boltzmann (LBM) code, verify it against analytic and host-side references, and compare it with the large-eddy simulation (LES) code MicroHH on closely related configurations. Heat and total water are not carried by FluidX3D's D3Q7 scalar lattices: we show by measurement that, as implemented, they diffuse with half the diffusivity the code sets, show an apparent excess of the fluid-cell scalar inventory next to walls in a buoyant flow near the stability limit, do not keep a uniform scalar uniform in a flow that is not divergence-free on seven points, and lose all diffusion when stored as 16-bit floats. Instead, both scalars are carried by a finite-volume scheme in conservative form whose advective fluxes are the net mass fluxes on the 18 links of the D3Q19 flow lattice, read from the post-collision populations. The scheme conserves the density-weighted scalar by construction in exact arithmetic (measured residual on the GPU 0.004 % over 20 000 steps), keeps a uniform scalar uniform, runs in any number of domains, and costs 1.7 times the D3Q7 lattices' time per step at 16 % less memory; with 16-bit storage of the flow populations a 5 m convective boundary layer of 172 million cells runs on one consumer GPU at 1660 million lattice updates per second. Verification: the thermal diffusivity within 0.2 %, the conserved heat inventory within 0.004 %, the added water within 0.001 %, the onset of Rayleigh-Bénard convection between Ra = 1600 and 1900, and the Nusselt number converging at first order to MicroHH's value in the same box. Comparison: the dry convective boundary layer of Sullivan and Patton (2011) at 10 m, a five-seed ensemble, differs from MicroHH on a related configuration by at most 3.2 % in the variance profiles over 0.1 to 0.8 zi; the entrainment ratio is -0.23 against -0.22. The moist boundary layer on a diurnal land sounding puts its cloud base within 3 % of the mixed layer's condensation level; its cover and its count of clouds larger than 0.01 km² lie in or just below the range MicroHH recorded, and it makes two to seven times fewer small clouds; that comparison is preliminary. The archive holds the LaTeX source, the data files, the figures and the scripts that regenerate them; the patch holds the code changes against the public FluidX3D-API fork at commit cec6842.