Improved parallel scaling of 3D Rayleigh-Benard convection simulations by parallelization in time

Rayleigh-Bénard convection (RBC) — the buoyancy-driven instability that arises when a fluid is heated from below and cooled from above, leading to the formation of convective plumes — serves as a fundamental and challenging benchmark problem in geophysical fluid dynamics. Simulating RBC at high Rayleigh numbers demands extremely fine spatial resolution, which in turn requires high-performance computing (HPC) resources to achieve results within feasible runtimes. However, strong parallel scaling based on spatial domain decomposition eventually saturates due to communication overheads, and simulations involving very large numbers of time steps can still be prohibitively time-consuming, with limited scope for further speedup through additional spatial parallelism.

To overcome these limitations, time-parallel algorithms — which introduce concurrency along the temporal dimension — offer a promising approach to extend strong scaling beyond the saturation of space-only parallelization. Despite their potential, constraints imposed by causality often make these methods challenging to design, and some classes of parallel-in-time algorithms can suffer from poor parallel efficiency. In contrast, parallel-across-the-method techniques, while providing only small-scale parallelism, tend to be easier to implement and can achieve competitive efficiency. Previous efforts to develop parallel Runge-Kutta methods were only moderately successful, primarily because the associated stability restrictions were more stringent than those of their serial counterparts.

Parallel Spectral Deferred Corrections (pSDC), however, enable parallel computation of stages without significantly reducing the maximum stable time step. In this talk, we introduce pSDC and present a bespoke solver that combines pSDC with parallel Fast Fourier Transforms (FFTs) on GPUs to facilitate efficient, large-scale simulations of RBC. We show performance results obtained on the JUWELS Booster and JUPITER HPC systems at the Jülich Supercomputing Centre, showcasing how pSDC can achieve runtime reductions beyond the limits of spatial parallelization alone.