# NekRS, a GPU-Accelerated Spectral Element Navier-Stokes Solver

arXiv: https://arxiv.org/abs/2104.05829 · HTML: https://mlsanity.com/paper/2104.05829/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Apr 2021.

## Built on by (most cited first, 8 of 8)

- [Mesh-based Super-Resolution of Fluid Flows with Multiscale Graph Neural Networks](https://mlsanity.com/paper/2409.07769/) (2024)
- [Curvature-Aware Optimization for High-Accuracy Physics-Informed Neural Networks](https://mlsanity.com/paper/2604.05230/) (2026)
- [Distributed Neural Representation for Reactive in situ Visualization](https://mlsanity.com/paper/2304.10516/) (2023)
- [Learning Turbulent Flows with Generative Models: Super-resolution, Forecasting, and Sparse Flow Reconstruction](https://mlsanity.com/paper/2509.08752/) (2025)
- [Uncertainty Quantification in PINNs for Turbulent Flows: Bayesian Inference and Repulsive Ensembles](https://mlsanity.com/paper/2604.17156/) (2026)
- [Scalable and Consistent Graph Neural Networks for Distributed Mesh-based Data-driven Modeling](https://mlsanity.com/paper/2410.01657/) (2024)
- [Super-resolution of turbulent reacting flows on complex meshes using graph neural networks](https://mlsanity.com/paper/2603.01080/) (2026)
- [Fixed-Budget Gaussian Volume Encoding with Structure-Aware Allocation](https://mlsanity.com/paper/2608.14112/) (2026)

## Abstract (arXiv)

The development of NekRS, a GPU-oriented thermal-fluids simulation code based on the spectral element method (SEM) is described. For performance portability, the code is based on the open concurrent compute abstraction and leverages scalable developments in the SEM code Nek5000 and in libParanumal, which is a library of high-performance kernels for high-order discretizations and PDE-based miniapps. Critical performance sections of the Navier-Stokes time advancement are addressed. Performance results on several platforms are presented, including scaling to 27,648 V100s on OLCF Summit, for calculations of up to 60B gridpoints.