GPU Performance of an Entropy-Stable Discontinuous Galerkin Euler Solver with Non-Conservative Terms
Abstract
The entropy-stable discontinuous Galerkin method for compressible Euler equations with buoyancy is implemented on graphics processing unit (GPU) hardware. We measure the performance of the solver on three-dimensional problems: the rising thermal bubble and the baroclinic instability in a channel. On NVIDIA A100 hardware, the solver achieves nearly 70\% of 64-bit floating-point peak performance for the most computationally expensive kernel (volume terms) and significantly reduces the computational overhead typically incurred by two point entropy-stable fluxes in the volume terms. We also present impressive strong and weak scaling performance of the solver and compare to a highly-optimized central processing unit (CPU) code showing that the GPU kernels are a factor of 10× faster and better than 13× more energy efficient than the CPU code. We also show that the solver achieves the expected 2× speedup when run at 32-bit floating-point peak performance. We discuss the different modifications that we implemented to reach the final form of the GPU implementation and measure the performance gain of each of the implementation strategies ranging from reduction in complex operations and memory traffic as well as load balancing. We also extend symmetry-based flux savings to the non-symmetric gravity term, preserving nearly the full factor-of-two speedup achieved for the symmetric flux.
Related
- Entropy-Stable and Well-Balanced Discontinuous Galerkin Methods for the Compressible Euler Equations in Vector-Invariant Form
- Fully discrete multi-entropy-stable compact Runge--Kutta discontinuous Galerkin methods for hyperbolic conservation laws
- A well-balanced path-conservative discontinuous Galerkin method with generalized hydrostatic reconstruction for non-conservative balance laws
- A class of high-order discontinuous-Galerkin methods satisfying infinitely many entropy conditions with provable error estimates and strong convergence for general nonlinear conservation laws
- Entropy bounded compact stencil Runge-Kutta discontinuous Galerkin method for hyperbolic conservation laws
BibTeX
@misc{waterhouse2026performance,
title = {{GPU Performance of an Entropy-Stable Discontinuous Galerkin Euler Solver with Non-Conservative Terms}},
author = {Henry Waterhouse and Maciej Waruszewski and Lucas C. Wilcox and Timothy Warburton and Francis X. Giraldo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.16684},
eprint = {2605.16684},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.16684},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - GPU Performance of an Entropy-Stable Discontinuous Galerkin Euler Solver with Non-Conservative Terms
AU - Henry Waterhouse
AU - Maciej Waruszewski
AU - Lucas C. Wilcox
AU - Timothy Warburton
AU - Francis X. Giraldo
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2605.16684
UR - https://arxiv.org/abs/2605.16684
AB - The entropy-stable discontinuous Galerkin method for compressible Euler equations with buoyancy is implemented on graphics processing unit (GPU) hardware. We measure the performance of the solver on three-dimensional problems: the rising thermal bubble and the baroclinic instability in a channel. On NVIDIA A100 hardware, the solver achieves nearly 70\% of 64-bit floating-point peak performance for the most computationally expensive kernel (volume terms) and significantly reduces the computational overhead typically incurred by two point entropy-stable fluxes in the volume terms. We also present impressive strong and weak scaling performance of the solver and compare to a highly-optimized central processing unit (CPU) code showing that the GPU kernels are a factor of 10× faster and better than 13× more energy efficient than the CPU code. We also show that the solver achieves the expected 2× speedup when run at 32-bit floating-point peak performance. We discuss the different modifications that we implemented to reach the final form of the GPU implementation and measure the performance gain of each of the implementation strategies ranging from reduction in complex operations and memory traffic as well as load balancing. We also extend symmetry-based flux savings to the non-symmetric gravity term, preserving nearly the full factor-of-two speedup achieved for the symmetric flux.
ER -