Space-Time Parallel Direct Numerical Simulation of Rayleigh-Bénard Convection
Abstract
Rayleigh-Bénard convection (RBC) is a model for turbulent flow and challenging to simulate by direct numerical simulation (DNS). Adequate resolution of all relevant length scales requires very fine grids in space and stability restrictions can dictate small step sizes. In this paper, we investigate the use of parallel spectral deferred correction (SDC) as a high-order time-stepping method to reduce wall-clock times of direct numerical simulation of RBC. Performance results on JUSUF (CPUs) and JUPITER (GPUs) with two different codes show parallel SDC can offer some concurrency along the temporal axis plus larger maximum stable time steps. Taken together, this allows for a reduction of wall-clock time required for simulations over one free-fall time by having to compute fewer steps and being able to mitigate the higher cost per time step through temporal parallelization.
Related
- A Massively Parallel Hybridizable Discontinuous Galerkin Solver for Direct Numerical Simulation of Compressible Flows on GPUs
- Controlling three-dimensional falling liquid films: from weighted-residual models to direct numerical simulation
- Direct Numerical Simulation of Thermoacoustically Unstable Flames Via Non-Drifting Acoustic Delay Characteristic Boundary Conditions
- Scalable Fully Implicit Runge-Kutta Solvers for Time-Dependent Rayleigh-Bénard Convection
- A second-order linear decoupled scheme with a relaxed zero-energy variable for Rayleigh-Bénard convection
BibTeX
@misc{saupe2026spacetime,
title = {{Space-Time Parallel Direct Numerical Simulation of Rayleigh-Bénard Convection}},
author = {Thomas Saupe and Thibaut Lunet and Mathis Bode and Robert Speck and Sebastian Götschel and Daniel Ruprecht},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17942},
eprint = {2610.17942},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17942},
}
RIS
TY - UNPB
TI - Space-Time Parallel Direct Numerical Simulation of Rayleigh-Bénard Convection
AU - Thomas Saupe
AU - Thibaut Lunet
AU - Mathis Bode
AU - Robert Speck
AU - Sebastian Götschel
AU - Daniel Ruprecht
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.17942
UR - https://arxiv.org/abs/2610.17942
AB - Rayleigh-Bénard convection (RBC) is a model for turbulent flow and challenging to simulate by direct numerical simulation (DNS). Adequate resolution of all relevant length scales requires very fine grids in space and stability restrictions can dictate small step sizes. In this paper, we investigate the use of parallel spectral deferred correction (SDC) as a high-order time-stepping method to reduce wall-clock times of direct numerical simulation of RBC. Performance results on JUSUF (CPUs) and JUPITER (GPUs) with two different codes show parallel SDC can offer some concurrency along the temporal axis plus larger maximum stable time steps. Taken together, this allows for a reduction of wall-clock time required for simulations over one free-fall time by having to compute fewer steps and being able to mitigate the higher cost per time step through temporal parallelization.
ER -