Computational geodynamics to model mantle convection and magma oceans with the thermal lattice Boltzmann method and strong scaling on exascale clusters

SUMMARY The thermal lattice method (TLBM) offers an alternative to classical PDE-based numerical methods for modelling planetary dynamics. It solves the lattice Boltzmann equation on a unitary discrete lattice which requires no matrix operations, and hence scales extremely well on HPC clusters. We describe the TLBM equations which are capable of modelling solid state mantle convection and turbulent magma ocean dynamics, and we present how to obtain the physical (dimensional) timescale from the lattice timescale (number of time steps), convert quantities in physical (dimensional) units ($\eta$, $\kappa$, $\sigma \dots$) to unitary (dimensionless) lattice units and strong scaling performance in 3-D to 300 K cores. We present examples to illustrate the use of the TLBM to model plate tectonics, 2-D and 3-D mantle convection, turbulent magma ocean dynamics and planetary accretion. We present a table of run times which demonstrate the TLBM’s high throughput performance. The TLBM’s performance enables 3-D global convection modelling of the whole mantle on a lattice with up to $\sim 2 \times 10^{11}$ grid points corresponding to a resolution of 3 km, and magma ocean dynamics modelling into the ultimate turbulent regime of $Ra \gtrsim 10^{14}$, to at least $Ra = 10^{15}$ (demonstrated to date in 2-D for an aspect ratio of 1), and projected to be possible up to $Ra=10^{18}$ in 2-D or $Ra=10^{15}$ in 3-D for low aspect ratio models. The TLBM is fast and makes it possible to run huge models which opens exascale computing to planetary dynamics research. We believe that the TLBM provides a valuable new means to advance geodynamical research into the future by enabling fast and high-resolution planetary dynamics simulations including of global mantle convection, magma ocean dynamics into the ultimate turbulent regime and planetary accretion.