A Massively Parallel Hybridizable Discontinuous Galerkin Solver for Direct Numerical Simulation of Compressible Flows on GPUs

[2608.27863] A Massively Parallel Hybridizable Discontinuous Galerkin Solver for Direct Numerical Simulation of Compressible Flows on GPUs Skip to main content Search Submit Donate Log in Mathematics > Numerical Analysis arXiv:2608.27863 (math) [Submitted on 28 Aug 2026] Title: A Massively Parallel Hybridizable Discontinuous Galerkin Solver for Direct Numerical Simulation of Compressible Flows on GPUs Authors: Andrew Welter , Thea Collin , Ngoc Cuong Nguyen , Jaime Peraire View PDF HTML (experimental) Abstract: Direct numerical simulation (DNS) of compressible transitional and turbulent flows requires numerical methods that combine high-order accuracy, robustness, and computational efficiency to resolve a broad range of spatial and temporal scales. This paper presents a massively parallel hybridizable discontinuous Galerkin (HDG) solver for DNS of the compressible Navier-Stokes equations on GPU-accelerated high-performance computing systems. The proposed solver combines high-order HDG discretization with robust shock capturing, diagonally implicit Runge-Kutta (DIRK) time integration, and an efficient Newton-GMRES solution strategy accelerated by additive Schwarz preconditioning and reduced-basis approximation. A distributed implementation of these methods based on GPU-aware MPI, Kokkos, and CUDA/HIP libraries enables scalable execution on heterogeneous computing platforms. The solver is demonstrated on three canonical benchmark problems covering a wide range of Mach-number flow regimes: subsonic transitional flow over the Eppler 387 airfoil, the supersonic Taylor-Green vortex, and hypersonic boundary-layer transition. Numerical results are compared with available experimental measurements and published DNS data, showing good agreement across distinct flow regimes. The results demonstrate the ability of the proposed solver to resolve laminar-turbulent transition, strong compressibility effects, shock-associated flow structures, and fully three-dimensional turbulent dynamics. Subjects: Numerical Analysis (math.NA) ; Fluid Dynamics (physics.flu-dyn) Cite as: arXiv:2608.27863 [math.NA] (or arXiv:2608.27863v1 [math.NA] for this version) https://doi.org/10.48550/arXiv.2608.27863 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Andrew Welter [ view email ] [v1] Fri, 28 Aug 2026 03:12:47 UTC (29,700 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.NA < prev | next > new | recent | 2026-08 Change to browse by: cs cs.NA math physics physics.flu-dyn References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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