The Thermal Lattice Boltzmann Method: new developments, strong scaling to 300K cores, and potential to yield major advancements in geodynamics

The Thermal Lattice Boltzmann Method (TLBM) offers an alternative to classical PDE based solvers for planetary dynamics and is based on solving the Boltzmann Equation on a discrete lattice which maps perfectly onto parallel computers. We present strong scaling performance runs on the Shaheen III HPC cluster at KAUST using up to 300K cores for a 3D whole mantle model at a 3km grid resolution. Based on the throughput performance achieved, the TLBM can model mantle simulation in 3D for one convection cycle's worth of physical time in less than a day of CPU at a 3km resolution. We present 2D performance results which indicate that the TLBM can model ultra-high Rayleigh numbers in 2D well into the ultimate turbulent regime up to Ra = 10¹⁸ on 300K cores in a 1x1 aspect ratio model. We also  present an update of the status of TLBM developments and example runs and run times of: (1) the transition to plate tectonics in the Archean using a temperature dependent viscosity, a yield stress formulation of the rheology and partial melting, (2) high Rayleigh number simulations in the turbulent regime up to Ra = 10¹⁵ in 2D, (3) 2D whole mantle modelling in a circular annulus and accuracy benchmarks against ASPECT, and (4)  3D simulations of whole mantle convection at a resolution of 30 km on just 96 cores, and (5) iron droplets from an impactor on a turbulent magma ocean settling to form the iron core using a combined TLBM and multiphase LBM. We believe that the TLBM and multiphase TLBM have the potential to lead to new insights in the dynamics and evolution of the Earth and exoplanets from the early lava world stage onwards including plate tectonics due to their high throughput performance and near linear scaling to 100s of K cores. These capabilities enable geodynamical modelling with never-before-seen resolutions in 2D and 3D, high Rayleigh numbers well into the ultimate turbulent regime, studies of turbulent magma oceans and core formation, and phase space studies of planetary dynamics.