Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

GPU-accelerated simulations of turbulence: Review of current applications and future perspectives

A. Roccon1,2, G. Amati3, L. Brandt4, D. Calhoun5, P. Costa6, W. Lu7, S. Pirozzoli8, D. Richter9, M. Umair10,11 et al.

D. You12, T. Zahtila13, and C. Marchioli1,*,†

  • *Contact author: marchioli@uniud.it
  • †Also at Department of Fluid Mechanics, CISM, 33100 Udine, Italy.

Phys. Rev. Fluids 11, 034905 – Published 23 March, 2026Erratum Phys. Rev. Fluids 11, 059901 (2026)

DOI: https://doi.org/10.1103/vz9c-bbzm

Abstract

The growing availability of GPU-accelerated open-source solvers has boosted the capability of tackling complex single-phase and multiphase turbulent flows by means of direct and large-eddy simulations. GPU-accelerated solvers can leverage the heterogeneous computing architectures that are available in leading high-performance computing centers worldwide, taking advantage of the higher throughput and greater energy efficiency offered by GPUs as compared to CPUs. However, porting CPU-based numerical solvers to GPUs entails many outstanding challenges, such as parallelism exposure, inter-GPU communication, memory allocation constraints, and shared memory limitations. To overcome these challenges, GPU-friendly algorithms, performance portability strategies, and careful selection of computational paradigms and programming languages must be developed. Besides, adaptive mesh refinement and data compression may be integrated to mitigate I-O bottlenecks and enable simulations of more complex geometries on top of the existing requirements imposed by incompressible flows. When compressibility effects become significant, further considerations related to the adoption of high-performance preconditioners and multigrid solvers become crucial for tackling large, sparse linear systems and extending simulations to high-Mach flows. Finally, reduced-precision arithmetic can further enhance performance, energy efficiency, and scalability. In this work, we survey current applications of GPU-accelerated solvers in the broad area of fluid mechanics and turbulence simulations and discuss the main challenges and bottlenecks associated with code porting and optimization. We then conclude our analysis with an outlook on future perspectives for enabling efficient GPU-based exascale computing of turbulence.

View figure in article

Physics Subject Headings (PhySH)

Erratum

Erratum: GPU-accelerated simulations of turbulence: Review of current applications and future perspectives [Phys. Rev. Fluids 11, 034905 (2026)]

A. Roccon, G. Amati, L. Brandt, D. Calhoun, P. Costa, W. Lu, S. Pirozzoli, D. Richter, M. Umair, D. You, T. Zahtila, and C. Marchioli
Phys. Rev. Fluids 11, 059901 (2026)

Article Text

References (290)

  1. W. Gao, W. Zhang, W. Cheng, and R. Samtaney, Wall-modelled large-eddy simulation of turbulent flow past airfoils, J. Fluid Mech. 873, 174 (2019).
  2. W. C. Reynolds, The potential and limitations of direct and large eddy simulations, in Whither Turbulence? Turbulence at the Crossroads, edited by J. L. Lumley, Lecture Notes in Physics Vol. 357 (Springer, Berlin, Heidelberg, 1990), p. 313.
  3. S. Pirozzoli and P. Orlandi, Natural grid stretching for DNS of wall-bounded flows, J. Comput. Phys. 439, 110408 (2021).
  4. TOP500 list, https://top500.org/lists/top500/.
  5. S. Matsuoka, Fugaku and A64FX: The first exascale supercomputer and its innovative ARM CPU, in Proceedings of the 2021 Symposium on VLSI Circuits (IEEE, Los Alamitos, CA, 2021), pp. 1–3.
  6. J. S. Vetter, E. P. DeBenedictis, and T. M. Conte, Architectures for the post-moore era, IEEE Micro. 37, 6 (2017).
  7. P. M. Kogge and W. J. Dally, Frontier vs the exascale report: Why so long? and are we really there yet? in Proceedings of the IEEE/ACM International Workshop on Performance Modeling, Benchmarking and Simulation of High Performance Computer Systems (PMBS'22) (IEEE, Los Alamitos, CA, 2022), pp. 26–35.
  8. W. Shin, J. B. White, W. Elwasif, R. F. Da Silva, C. Zimmer, B. Messer, R. Budiardja, A. Georgiadou, V. M. Vergara, J. Lange, et al., Towards sustainable post-exascale leadership computing, in Proceedings of the Supercomputing Conference (SC24) (IEEE, Los Alamitos, CA, 2024), pp. 1790–1794.
  9. W. Shin, V. Oles, A. M. Karimi, J. A. Ellis, and F. Wang, Revealing power, energy and thermal dynamics of a 200PF pre-exascale supercomputer, in Proceedings of the Supercomputing Conference (SC'21) (IEEE, Los Alamitos, CA, 2021), pp. 1–14.
  10. X. Yang, W. Zhang, M. Abkar, and W. Anderson, Computational fluid dynamics: Its carbon footprint and role in carbon reduction, J. Renew. Sustain. Energy 16, 055906 (2024).
  11. L. Bertaccini, G. Paulin, T. Fischer, S. Mach, and L. Benini, MiniFloat-NN and ExSdotp: An ISA extension and a modular open hardware unit for low-precision training on RISC-V cores, in Proceedings of the IEEE 29th Symposium on Computer Arithmetic (ARITH) (IEEE, Los Alamitos, CA, 2022), pp. 1–8.
  12. F. Brogi, S. Bnà, G. Boga, G. Amati, T. E. Ongaro, and M. Cerminara, On floating point precision in computational fluid dynamics using OpenFOAM, Future Gener. Comput. Syst. 152, 1 (2024).
  13. A. Bhatnagar, V. Pandey, P. Perlekar, and D. Mitra, Rate of formation of caustics in heavy particles advected by turbulence, Philos. Trans. R. Soc. A 380, 20210086 (2022).
  14. Nvidia blackwell specs, https://resources.nvidia.com/en-us-blackwell-architecture.
  15. C. Marchioli, M. Bourgoin, F. Coletti, R. Fox, J. Magnaudet, M. Reeks, O. Simonin, M. Sommerfeld, F. Toschi, L.-P. Wang, and S. Balachandar, Particle-laden flows, Int. J. Multiphase Flow 191, 105291 (2025).
  16. O. M. H. Rodriguez, P. Angeli, D. Legendre, E. Climent, and A. Soldati, Drop-laden flows, Int. J. Multiphase Flow 191, 105284, (2025).
  17. M. Garcia-Villalba, T. Colonius, O. Desjardins, D. Lucas, A. Mani, D. Marchisio, O. K. Matar, F. Picano, and S. Zaleski, Numerical methods for multiphase flows, Int. J. Multiphase Flow 191, 105285 (2025).
  18. K. Rupp, Microprocessor trend data, https://github.com/karlrupp/microprocessor-trend-data.
  19. M. Louboutin, M. Lange, F. J. Herrmann, N. Kukreja, and G. Gorman, Performance prediction of finite-difference solvers for different computer architectures, Comput. Geosci. 105, 148 (2017).
  20. Y. Chen, P. de Oliveira Castro, P. Bientinesi, N. Jansson, and R. Iakymchuk, Enabling mixed-precision in spectral element codes, Future Gener. Comp. Sy. 174, 107990 (2025).
  21. W. A. Wulf and S. A. McKee, Hitting the memory wall: Implications of the obvious, ACM SIGARCH Comput. Archit. News 23, 20 (1995).
  22. S. A. McKee, Reflections on the memory wall, in Proceedings of the 1st Conference on Computing Frontiers (ACM Press, New York, 2004), p. 162.
  23. A. Gholami, Z. Yao, S. Kim, C. Hooper, M. W. Mahoney, and K. Keutzer, AI and memory wall, IEEE Micro. 44, 33 (2024).
  24. S. Williams, A. Waterman, and D. Patterson, Roofline: An insightful visual performance model for multicore architectures, Commun. ACM 52, 65 (2009).
  25. G. Ofenbeck, R. Steinmann, V. Caparros, D. G Spampinato, and M. Püschel, Applying the roofline model, in Proceedings of the IEEE ISPASS 2014 (IEEE, Los Alamitos, CA, 2014), pp. 76–85.
  26. J. Jeffers and J. Reinders, High Performance Parallelism Pearls Volume Two: Multicore and Many-core Programming Approaches (Morgan Kaufmann, Burlington, MA, 2015).
  27. B. Mostafazadeh, F. Marti, F. Liu, and A. Chandramowlishwaran, Roofline guided design and analysis of a multi-stencil CFD solver for multicore performance, in Proceedings of the 2018 IEEE IPDPS (IEEE, Los Alamitos, CA, 2018), pp. 753–762.
  28. D. M. Tullsen, S. J. Eggers, and H. M. Levy, Simultaneous multithreading: Maximizing on-chip parallelism, in Proceedings of the 22nd Annual International Symposium on Computer Architecture (IEEE, Los Alamitos, CA, 1995), pp. 392–403.
  29. S. J. Eggers, J. S. Emer, H. M. Levy, J. L. Lo, R. L. Stamm, and D. M. Tullsen, Simultaneous multithreading: A platform for next-generation processors, IEEE Micro. 17, 12 (1997).
  30. M. Bernaschi, M. Fatica, S. Melchionna, S. Succi, and E. Kaxiras, A flexible high-performance lattice Boltzmann GPU code for the simulations of fluid flows in complex geometries, Concurr. Comput. Pract. Exper. 22, 1 (2010).
  31. K. E. Niemeyer and C.-J. Sung, Recent progress and challenges in exploiting graphics processors in computational fluid dynamics, J. Supercomput. 67, 528 (2014).
  32. The die is the physical piece of silicon that contains the GPU's circuits, cores, caches, memory controllers, and other components. A die shot shows the layout of all these components as seen under a microscope or using specialized imaging equipment.
  33. NVIDIA, P. Vingelmann, and F. H. P. Fitzek, CUDA (2020), https://developer.nvidia.com/cuda/toolkit.
  34. M. Fatica and G. Ruetsch, CUDA Fortran for Scientists and Engineers, Best Practices for Efficient CUDA Fortran Programming (Morgan Kaufmann, Waltham, MA, 2014).
  35. AMD. HIP documentation, https://rocm.docs.amd.com/projects/HIP/en/latest/.
  36. J. E. Stone, D. Gohara, and G. Shi, OpenCL: A parallel programming standard for heterogeneous computing systems, J. Parallel Distrib. Comput. 12, 66, (2010).
  37. L. Dagum and R. Menon, OpenMP: an industry standard API for shared-memory programming, Comput. Sci. Eng. 5, 46 (1998).
  38. OpenACC working group , The OpenACC application programming interface (2011), https://www.openacc.org.
  39. H. C. Edwards, C. R. Trott, and J. Sunderland, Kokkos: Enabling manycore performance portability through polymorphic memory access patterns, J. Parallel Distrib. Comput. 74, 3202 (2014).
  40. Intel, The oneapi implementation of sycl, https://www.intel.com/content/www/us/en/developer/tools/oneapi/data-parallel-c-plus-plus.html.
  41. Khronos, C++ programming for heterogeneous parallel computing, https://www.khronos.org/sycl/.
  42. GPU vendor/programming model compatibility overview, https://github.com/AndiH/gpu-lang-compat.
  43. A. J. Chorin, Numerical solution of the Navier-Stokes equations, Math. Comp. 22, 745 (1968).
  44. J. Kim and P. Moin, Application of a fractional-step method to incompressible Navier-Stokes equations, J. Comput. Phys. 59, 308 (1985).
  45. P. J. Blair, An analysis of the fractional step method, J. Comput. Phys. 108, 51 (1993).
  46. X. Zhu, E. Phillips, V. Spandan, J. Donners, G. Ruetsch, J. Romero, R. Ostilla-Mónico, Y. Yang, D. Lohse, and R. Verzicco, AFiD-GPU: A versatile Navier–Stokes solver for wall-bounded turbulent flows on GPU clusters, Comput. Phys. Commun. 229, 199 (2018).
  47. P. Costa, A FFT-based finite-difference solver for massively-parallel direct numerical simulations of turbulent flows, Comput. Math. Appl. 76, 1853 (2018).
  48. P. Costa, E. Phillips, L. Brandt, and M. Fatica, GPU acceleration of CaNS for massively-parallel direct numerical simulations of canonical fluid flows, Comput. Math. Appl. 81, 502 (2021).
  49. D. Mierke, C. F. Janßen, and T. Rung, An efficient algorithm for the calculation of sub-grid distances for higher-order LBM boundary conditions in a GPU simulation environment, Comput. Math. Appl. 79, 66 (2020).
  50. B. Fryxell, K. Olson, P. Ricker, F. X. Timmes, M. Zingale, D. Q. Lamb, P. MacNeice, R. Rosner, J. W. Truran, and H. Tufo, FLASH: An adaptive mesh hydrodynamics code for modeling astrophysical thermonuclear flashes, Astrophys. J. Suppl. Ser. 131, 273 (2000).
  51. A. Dubey, K. Weide, J. O Neal, A. Dhruv, S. Couch, J. A. Harris, T. Klosterman, R. Jain, J. Rudi, B. Messer, et al., Flash-X: A multiphysics simulation software instrument, SoftwareX 19, 101168 (2022).
  52. A. Roccon, G. Soligo, and A. Soldati, FLOW36: A spectral solver for phase-field based multiphase turbulence simulations on heterogeneous computing architectures, Comput. Phys. Commun. 313, 109640 (2025).
  53. M. Crialesi-Esposito, N. Scapin, A. D. Demou, M. E. Rosti, P. Costa, F. Spiga, and L. Brandt, FluTAS: A GPU-accelerated finite difference code for multiphase flows, Comput. Phys. Commun. 284, 108602 (2023).
  54. G. Bilotta, From GPU to CPU (and beyond): Extending hardware support in GPUSPH through a SYCL-inspired interface, Concur. Comp. Pract. E 37, e8313 (2025).
  55. A. Roccon, L. Enzenberger, D. Zaza, and A. Soldati, MHIT36: A phase-field code for GPU simulations of multiphase homogeneous isotropic turbulence, Comput. Phys. Commun. 316, 109804, (2025).
  56. A. Roccon, MHIT36: Extension to wall-bounded turbulence and scalar transport equation, Comput. Phys. Commun. 320, 109956 (2026).
  57. N. Jansson, M. Karp, A. Podobas, S. Markidis, and P. Schlatter, Neko: A modern, portable, and scalable framework for high-fidelity computational fluid dynamics, Comput. Fluids 275, 106243 (2024).
  58. N. Jansson, M. Karp, J. Wahlgren, S. Markidis, and P. Schlatter, Design of Neko: A scalable high-fidelity simulation framework with extensive accelerator support, Concurr. Comput. Pract. Exp. 37, e8340 (2025).
  59. P. Fischer, S. Kerkemeier, M. Min, Y.-H. Lan, M. Phillips, T. Rathnayake, E. Merzari, A. Tomboulides, A. Karakus, and N. Chalmers, NekRS, a GPU-accelerated spectral element Navier–Stokes solver, Parallel Comput. 114, 102982 (2022).
  60. J. M. López, D. Feldmann, M. Rampp, A. Vela-Martín, L. Shi, and M. Avila, nsCouette–a high-performance code for direct numerical simulations of turbulent Taylor–Couette flow, SoftwareX 11, 100395 (2020).
  61. A. Ramadhan, G. Wagner, C. Hill, J.-M. Campin, V. Churavy, T. Besard, A. Souza, A. Edelman, R. Ferrari, and J. Marshall, Oceananigans.jl: Fast and friendly geophysical fluid dynamics on GPUs, J. Open Source Softw. 5, 2018 (2020).
  62. V. Heuveline and J. Latt, The OpenLB project: An open source and object oriented implementation of lattice Boltzmann methods, Int. J. Mod. Phys. C 18, 627 (2007).
  63. J. Latt, O. Malaspinas, D. Kontaxakis, A. Parmigiani, D. Lagrava, F. Brogi, M. B. Belgacem, Y. Thorimbert, S. Leclaire, S. Li, et al., Palabos: Parallel lattice Boltzmann solver, Comput. Math. Appl. 81, 334 (2021).
  64. J. Latt and C. Coreixas, Multi-GPU acceleration of PALABOS fluid solver using C standard parallelism, Comput. Phys. Commun. 323, 110094 (2026).
  65. L. Gasparino, F. Spiga, and O. Lehmkuhl, SOD2D: A GPU-enabled spectral finite elements method for compressible scale-resolving simulations, Comput. Phys. Commun. 297, 109067 (2024).
  66. M. Mortensen and H. P. Langtangen, High performance Python for direct numerical simulations of turbulent flows, Comput. Phys. Commun. 203, 53 (2016).
  67. T. D. Economon, F. Palacios, S. R. Copeland, T. Lukaczyk, and J. J. Alonso, SU2: An open-source suite for multiphysics simulation and design, AIAA J. 54, 828 (2016).
  68. M. Bauer, S. Eibl, C. Godenschwager, N. Kohl, M. Kuron, C. Rettinger, F. Schornbaum, C. Schwarzmeier, D. Thönnes, H. Köstler, et al., waLBerla: A block-structured high-performance framework for multiphysics simulations, Comput. Math. Appl. 81, 478 (2021).
  69. WaterLily.jl: A differentiable fluid simulator in Julia with fast heterogeneous execution, Comput. Phys. Commun. 315, 109748 (2025).
  70. P. Bartholomew, G. Deskos, R. A. S. Frantz, F. N. Schuch, E. Lamballais, and S. Laizet, Xcompact3D: An open-source framework for solving turbulence problems on a Cartesian mesh, SoftwareX 12, 100550 (2020).
  71. P. M. Gresho and S. T. Chan, On the theory of semi-implicit projection methods for viscous incompressible flow and its implementation via a finite element method that also introduces a nearly consistent mass matrix. Part 2: Implementation, Int. J. Numer. Methods Fluids 11, 621 (1990).
  72. H. Le and P. Moin, An improvement of fractional step methods for the incompressible Navier-Stokes equations, J. Comput. Phys. 92, 369 (1991).
  73. S. Hahn, J. Je, and H. Choi, Direct numerical simulation of turbulent channel flow with permeable walls, J. Fluid Mech. 450, 259 (2002).
  74. H. Abe, H. Kawamura, and Y. Matsuo, Direct numerical simulation of a fully developed turbulent channel flow with respect to the Reynolds number dependence, J. Fluids Eng. 123, 382 (2001).
  75. S. V. Patankar and D. B. Spalding, A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows, in Numerical Prediction of Flow, Heat Transfer, Turbulence and Combustion (Elsevier, Amsterdam, 1983), pp. 54–73.
  76. J. Kim, P. Moin, and R. Moser, Turbulence statistics in fully developed channel flow at low Reynolds number, J. Fluid Mech. 177, 133 (1987).
  77. P. R. Spalart, Direct simulation of a turbulent boundary layer up to Reθ=1410, J. Fluid Mech. 187, 61 (1988).
  78. P. F. Fischer, L. W. Ho, G. E. Karniadakis, E. M. Conquest, and A. T. Patera, Recent advances in parallel spectral element simulation of unsteady incompressible flows, in Computational Structural Mechanics & Fluid Dynamics (Pergamon Press, Oxford, 1988), pp. 217–231.
  79. S. Mittal and V. Kumar, Finite element study of vortex-induced cross-flow and in-line oscillations of a circular cylinder at low Reynolds numbers, Int. J. Numer. Methods Fluids 31, 1087 (1999).
  80. A. T. Patera, A spectral element method for fluid dynamics: Laminar flow in a channel expansion, J. Comput. Phys. 54, 468 (1984).
  81. Y. Maday and A. T. Patera, Spectral element methods for the incompressible Navier-Stokes equations, in State-of-the-art Surveys on Computational Mechanics (A90-47176 21-64) (ASME, New York, 1989), pp. 71–143.
  82. R. G. Jacobs and P. A. Durbin, Simulations of bypass transition, J. Fluid Mech. 428, 185 (2001).
  83. J. Kim, D. Kim, and H. Choi, An immersed-boundary finite-volume method for simulations of flow in complex geometries, J. Comput. Phys. 171, 132 (2001).
  84. T. S. Lund, X. Wu, and K. D. Squires, Generation of turbulent inflow data for spatially-developing boundary layer simulations, J. Comput. Phys. 140, 233 (1998).
  85. H. Sanghyun, P. Junshin, and Y. Donghyun, A GPU-accelerated semi-implicit fractional-step method for numerical solutions of incompressible Navier–Stokes equations, J. Comput. Phys. 352, 246 (2018).
  86. G. Alfonsi, S. A. Ciliberti, M. Mancini, and L. Primavera, GPGPU implementation of mixed spectral-finite difference computational code for the numerical integration of the three-dimensional time-dependent incompressible Navier Stokes equations, Comput. Fluids 102, 237 (2014).
  87. F. Salvadore, M. Bernardini, and M. Botti, GPU accelerated flow solver for direct numerical simulation of turbulent flows, J. Comput. Phys. 235, 129 (2013).
  88. S. P. Vanka, A. F. Shinn, and K. C. Sahu, Computational fluid dynamics using graphics processing units: Challenges and opportunities, in Proceedings of the ASME International Mechanical Engineering Congress and Exposition (ASME, New York, 2011), Vol. 54921, p. 429.
  89. H. Zolfaghari, B. Becsek, M. G. Nestola, W. B. Sawyer, R. Krause, and D. Obrist, High-order accurate simulation of incompressible turbulent flows on many parallel GPUs of a hybrid-node supercomputer, Comput. Phys. Commun. 244, 132 (2019).
  90. M. Di Renzo, L. Fu, and J. Urzay, HTR solver: An open-source exascale-oriented task-based multi-GPU high-order code for hypersonic aerothermodynamics, Comput. Phys. Commun. 255, 107262 (2020).
  91. M. Bernardini, D. Modesti, F. Salvadore, and S. Pirozzoli, STREAmS: A high-fidelity accelerated solver for direct numerical simulation of compressible turbulent flows, Comput. Phys. Commun. 263, 107906 (2021).
  92. J. Thibault and I. Senocak, CUDA implementation of a Navier-Stokes solver on multi-GPU desktop platforms for incompressible flows, in Proceedings of the 47th AIAA Aerospace Sciences Meeting (AIAA, Reston, VA, 2009), p. 758.
  93. D. Jacobsen, J. Thibault, and I. Senocak, An MPI-CUDA implementation for massively parallel incompressible flow computations on multi-GPU clusters, in Proceedings of the 48th AIAA Aerospace Sciences Meeting (AIAA, Reston, VA, 2010), p. 522.
  94. H. Cheng, M. Grossman, and T. McKercher, Professional CUDA C Programming (John Wiley & Sons, New York, 2014).
  95. D. B. Kirk and W. H. Wen-Mei, Programming Massively Parallel Processors: A Hands-on Approach (Morgan Kaufmann, Waltham, MA, 2016).
  96. G. Ruetsch and M. Fatica, CUDA Fortran for Scientists and Engineers: Best Practices for Efficient CUDA Fortran Programming (Elsevier, Amsterdam, 2024).
  97. S. Ha, J. Park, and D. You, A multi-GPU method for ADI-based fractional-step integration of incompressible Navier-Stokes equations, Comput. Phys. Commun. 265, 107999 (2021).
  98. X. H. Sun, H. Z. Sun, and L. M. Ni, Parallel algorithms for solution of tridiagonal systems on multicomputers, in Proceedings of the International Conference on Supercomputing (ACM Press, New York, 1989), pp. 303–312.
  99. E. Laszlo, M. Giles, and J. Appleyard, Manycore algorithms for batch scalar and block tridiagonal solvers, ACM Trans. Math. Softw. 42, 1 (2016).
  100. K. H. Kim, J. H. Kang, X. Pan, and J. I. Choi, PaScaL_TDMA: A library of parallel and scalable solvers for massive tridiagonal systems, Comput. Phys. Commun. 260, 107722 (2021).
  101. R. D. Sanhueza, J. Peeters, and P. Costa, A pencil-distributed finite-difference solver for extreme-scale calculations of turbulent wall flows at high Reynolds number, Comput. Phys. Comm. 316, 109811 (2025).
  102. L. N. Trefethen, Spectral Methods in MATLAB (SIAM, Philadelphia, PA, 2000).
  103. K. Ravikumar, D. Appelhans, and P. K. Yeung, GPU acceleration of extreme scale pseudo-spectral simulations of turbulence using asynchronism, in Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis (ACM Press, New York, 2019), pp. 1–22.
  104. P. K. Yeung, K. Ravikumar, S. Nichols, and R. Uma-Vaideswaran, GPU-enabled extreme-scale turbulence simulations: Fourier pseudo-spectral algorithms at the exascale using OpenMP offloading, Comput. Phys. Commun. 306, 109364 (2025).
  105. C. Cecka, A. J. Lew, and E. Darve, Assembly of finite element methods on graphics processors, Int. J. Numer. Methods Eng. 85, 640 (2011).
  106. N. S.-C. Kao and T. W.-H. Sheu, Development of a finite element flow solver for solving three-dimensional incompressible Navier–Stokes solutions on multiple GPU cards, Comput. Fluids 167, 285 (2018).
  107. M. U. Zapata, F. J. Hernandez-Lopez, and R. I. Balam, A parallel unstructured multi-color SOR solver for 3D Navier–Stokes equations on graphics processing units, Comput. Fluids 260, 105909 (2023).
  108. R. Borrell, D. Dosimont, M. Garcia-Gasulla, G. Houzeaux, O. Lehmkuhl, V. Mehta, H. Owen, M. Vázquez, and G. Oyarzun, Heterogeneous CPU/GPU co-execution of CFD simulations on the POWER-9 architecture: Application to airplane aerodynamics, Future Gener. Comput. Syst. 107, 31 (2020).
  109. H. Owen, D. Ernst, T. Gruber, O. Lemkuhl, G. Houzeaux, L. Gasparino, and G. Wellein, Alya towards exascale: Optimal OpenACC performance of the Navier-Stokes finite element assembly on GPUs, in Proceedings of the IEEE International Symposium on Parallel and Distributed Processing (IPDPS'24) (IEEE, Los Alamitos, CA, 2024), pp. 408–416.
  110. H. Owen, O. Lehmkuhl, P. D'Ambra, F. Durastante, and S. Filippone, Alya toward exascale: Algorithmic scalability using psctoolkit, J. Supercomput. 80, 13533 (2024).
  111. C. D. Cantwell, D. Moxey, A. Comerford, A. Bolis, G. Rocco, G. Mengaldo, D. De Grazia, S. Yakovlev, J.-E. Lombard, and D. Ekelschot, Nektar: An open-source spectral/hp element framework, Comput. Phys. Commun. 192, 205 (2015).
  112. D. Moxey, C. D. Cantwell, Y. Bao, A. Cassinelli, G. Castiglioni, S. Chun, E. Juda, E. Kazemi, K. Lackhove, and J. Marcon, Nektar: Enhancing the capability and application of high-fidelity spectral/hp element methods, Comput. Phys. Commun. 249, 107110 (2020).
  113. H. M. Blackburn, D. Lee, T. Albrecht, and J. Singh, Semtex: A spectral element–Fourier solver for the incompressible Navier–Stokes equations in cylindrical or cartesian coordinates, Comput. Phys. Commun. 245, 106804 (2019).
  114. A. Abdelfattah, V. Barra, N. Beams, R. Bleile, J. Brown, J.-S. Camier, R. Carson, N. Chalmers, V. Dobrev, and Y. Dudouit, GPU algorithms for efficient exascale discretizations, Parallel Comput. 108, 102841 (2021).
  115. S. Markidis, J. Gong, M. Schliephake, E. Laure, A. Hart, D. Henty, K. Heisey, and P. Fischer, OpenACC acceleration of the Nek5000 spectral element code, Int. J. High Perform. Comput. Appl. 29, 311 (2015).
  116. M. Otten, J. Gong, A. Mametjanov, A. Vose, J. Levesque, P. Fischer, and M. Min, An MPI/OpenACC implementation of a high-order electromagnetics solver with GPUDirect communication, Int. J. High Perform. Comput. Appl. 30, 320 (2016).
  117. J. Gong, S. Markidis, E. Laure, M. Otten, P. Fischer, and M. Min, Nekbone performance on GPUs with OpenACC and CUDA fortran implementations, J. Supercomput. 72, 4160 (2016).
  118. E. Otero, J. Gong, M. Min, P. Fischer, P. Schlatter, and E. Laure, OpenACC acceleration for the PN–PN-2 algorithm in Nek5000, J. Parallel Distrib. Comput. 132, 69 (2019).
  119. M. Karp, N. Jansson, A. Podobas, P. Schlatter, and S. Markidis, Optimization of tensor-product operations in nekbone on GPUs, in Proceedings of the International Conference for High Performance Computing, Networking, Storage, and Analysis (SC20) (ACM Press, New York, 2020).
  120. J. Vincent, J. Gong, M. Karp, A. Peplinski, N. Jansson, A. Podobas, A. Jocksch, J. Yao, F. Hussain, and S. Markidis, Strong scaling of OpenACC enabled Nek5000 on several GPU based HPC systems, in Proceedings of the Supercomputing Asia and International Conference on High Performance Computing in Asia Pacific Region Workshops (ACM Press, New York, 2022), pp. 94–102.
  121. M. Karp, Direct numerical simulation of turbulence on heterogenous computer systems, Ph.D. thesis, KTH Royal Institute of Technology, 2024.
  122. D. S. Medina, A. St-Cyr, and T. Warburton, OCCA: A unified approach to multi-threading languages, arXiv:1403.0968.
  123. W. Lu, D. Aljubaili, T. Zahtila, L. Chan, and A. Ooi, Asymmetric wakes in flows past circular cylinders confined in channels, J. Fluid Mech. 958, A8 (2023).
  124. T. Zahtila, L. Chan, A. Ooi, K. Liu, M. Benjamin, and G. Iaccarino, Influence of miura-origami shapes on drag in turbulent flows, in Proceedings of the Summer Program 2022 for the Center for Turbulence Research (Stanford University, Center for Turbulence Research, Stanford, CA, 2022).
  125. D. Reger, E. Merzari, T. Nguyen, Y.-H. Lan, P. Fischer, and Y. Hassan, A study of the transition to turbulence in a bed of 67 spherical pebbles, Flow Turb. Comb. 114, 765 (2024).
  126. W. Lu, L. Chan, and A. Ooi, Spectral analysis of confined cylinder wakes, Fluids 10, 84 (2025).
  127. P.-H. Tsai, P. Fischer, and T. Iliescu, A time-relaxation reduced order model for the turbulent channel flow, J. Comput. Phys. 521, 113563 (2025).
  128. W. Lu, T. Zahtila, L. Chan, Q. D. Nguyen, C. Lei, G. Iaccarino, and A. Ooi, Modeling of uncertainties from spanwise asymmetries in upstream conditions and measurement plane location for flow past a circular cylinder confined within a duct, Phys. Rev. Fluids 10, 064601 (2025).
  129. D. Massaro, M. Karp, N. Jansson, S. Markidis, and P. Schlatter, Direct numerical simulation of the turbulent flow around a flettner rotor, Sci. Rep. 14, 3004 (2024).
  130. M. Gomez-Gesteira, A. J. C. Crespo, B. D. Rogers, R. A. Dalrymple, J. M. Dominguez, and A. Barreiro, SPHysics—Development of a free-surface fluid solver-Part 2: Efficiency and test cases, Comput. Geosci. 48, 300 (2012).
  131. A. Montessori, M. Lauricella, A. Tiribocchi, M. Durve, M. La Rocca, G. Amati, F. Bonaccorso, and S. Succi, Thread-safe lattice Boltzmann for high-performance computing on GPUs, J. Comput. Sci. 74, 102165 (2023).
  132. M. Lauricella, A. Mukherjee, L. Brandt, S. Succi, D. Izbassarov, and A. Montessori, accLB: A high-performance lattice-Boltzmann code for multiphase turbulence on multi-GPU architectures, Proc. Comput. Sci. 267, 40 (2025).
  133. G. Amati, S. Succi, and R. Piva, Massively parallel lattice-Boltzmann simulation of turbulent channel flow, Int. J. Mod. Phys. C 08, 869 (1997).
  134. H. Chen, S. Kandasamy, S. Orszag, R. Shock, S. Succi, and V. Yakhot, Extended Boltzmann kinetic equation for turbulent flows, Science 301, 633 (2003).
  135. C. Peng, N. Geneva, Z. Guo, and L.-P. Wang, Direct numerical simulation of turbulent pipe flow using the lattice Boltzmann method, J. Comput. Phys. 357, 16 (2018).
  136. S. A Orszag and G. S. Patterson Jr, Numerical simulation of three-dimensional homogeneous isotropic turbulence, Phys. Rev. Lett. 28, 76 (1972).
  137. Y. Li, E. Perlman, M. Wan, Y. Yang, C. Meneveau, R. Burns, S. Chen, A. Szalay, and G. Eyink, A public turbulence database cluster and applications to study Lagrangian evolution of velocity increments in turbulence, J. Turbul. 9, N31 (2008).
  138. P. K. Yeung, K. Ravikumar, R. Uma-Vaideswaran, D. L. Dotson, K. R. Sreenivasan, S. B. Pope, C. Meneveau, and S. Nichols, Small-scale properties from exascale computations of turbulence on a periodic cube, J. Fluid Mech. 1019, R2 (2025).
  139. D. Modesti and S. Pirozzoli, Direct numerical simulation of forced thermal convection in square ducts up to Reτ≈2000, J. Fluid Mech. 941, A16 (2022).
  140. S. Pirozzoli, On the streamwise velocity variance in the near-wall region of turbulent flows, J. Fluid Mech. 989, A5 (2024).
  141. G. A. Voth and A. Soldati, Anisotropic particles in turbulence, Annu. Rev. Fluid Mech. 49, 249 (2017).
  142. F. Risso, Agitation, mixing, and transfers induced by bubbles, Annu. Rev. Fluid Mech. 50, 25 (2018).
  143. J. Wang, M. Alipour, G. Soligo, A. Soldati, M. De Paoli, F. Picano, and A. Soldati, Short-range exposure to airborne virus transmission and current guidelines, Proc. Natl. Acad. Sci. USA 118, e2105279118 (2021).
  144. L. Bourouiba, The fluid dynamics of disease transmission, Annu. Rev. Fluid Mech. 53, 473 (2021).
  145. L. Deike, Mass transfer at the ocean–atmosphere interface: The role of wave breaking, droplets, and bubbles, Annu. Rev. Fluid Mech. 54, 191 (2022).
  146. F. Viola, G. Del Corso, R. De Paulis, and R. Verzicco, GPU accelerated digital twins of the human heart open new routes for cardiovascular research, Sci. Rep. 13, 8230 (2023).
  147. C. Marchioli, M. E. Rosti, and G. Verhille, Flexible fibers in turbulence, Annu. Rev. Fluid Mech. 58, 167 (2026).
  148. G. Soligo, A. Roccon, and A. Soldati, Effect of surfactant-laden droplets on turbulent flow topology, Phys. Rev. Fluids 5, 073606 (2020).
  149. G. Lupo, P. Wellens, and P. Costa, CaNS-Fizzy: A GPU-accelerated finite difference solver for turbulent two-phase flows, J. Open Source Soft. 10, 8076 (2025).
  150. A. M. Bilondi, N. Scapin, L. Brandt, and P. Mirbod, Turbulent convection in emulsions: The Rayleigh–Bénard configuration, J. Fluid Mech. 999, A4 (2024).
  151. H.-R. Liu, K. L. Chong, C. S. Ng, R. Verzicco, and D. Lohse, Enhancing heat transport in multiphase Rayleigh–Bénard turbulence by changing the plate–liquid contact angles, J. Fluid Mech. 933, R1 (2022).
  152. D. J. Dhas and C. Marchioli, Orientational dynamics of long flexible fibers in wall-bounded turbulence, J. Fluids Eng. 147, 071102 (2025).
  153. D. Di Giusto and C. Marchioli, Turbulence modulation by slender fibers, Fluids 7, 255 (2022).
  154. W. Su, H. Zhang, S. Fu, X. Xiang, and L. Wang, Particle-resolved direct numerical simulation of particle-laden turbulence modulation with high stokes number monodisperse spheres, Phys. Fluids 35, 105120 (2023).
  155. P. Karnakov, F. Wermelinger, S. Litvinov, and P. Koumoutsakos, Aphros: High performance software for multiphase flows with large scale bubble and drop clusters, in Proceedings of the Platform for Advanced Scientific Computing Conference (PASC20) (ACM Press, New York, 2020), pp. 1–10.
  156. R. Porcu, J. Musser, A. S. Almgren, J. B. Bell, W. D. Fullmer, and D. Rangarajan, MFIX-Exa: CFD-DEM simulations of thermodynamics and chemical reactions in multiphase flows, Chem. Eng. Sci. 273, 118614 (2023).
  157. P. Zaspel and M. Griebel, Solving incompressible two-phase flows on multi-GPU clusters, Comput. Fluids 80, 356 (2013).
  158. W. Aniszewski, T. Arrufat, M. Crialesi-Esposito, S. Dabiri, D. Fuster, Y. Ling, J. Lu, L. Malan, S. Pal, and R. Scardovelli, Parallel, robust, interface simulator (PARIS), Comput. Phys. Commun. 263, 107849 (2021).
  159. F. Pelusi, M. Lulli, M. Sbragaglia, and M. Bernaschi, TLBfind: A thermal lattice Boltzmann code for concentrated emulsions with FINite-size droplets, Comput. Phys. Commun. 273, 108259 (2022).
  160. T. Brandvik and G. Pullan, Acceleration of a 3D euler solver using commodity graphics hardware, in Proceedings of the 46th AIAA Aerospace Sciences Meeting (AIAA, Reston, VA, 2008), p. 607.
  161. E. Elsen, P. LeGresley, and E. Darve, Large calculation of the flow over a hypersonic vehicle using a GPU, J. Comput. Phys. 227, 10148 (2008).
  162. A. Corrigan, F. F. Camelli, R. Löhner, and J. Wallin, Running unstructured grid-based CFD solvers on modern graphics hardware, Int. J. Numer. Methods Fluids 66, 221 (2011).
  163. G. Dang, S. Liu, T. Guo, J. Duan, and X. Li, Direct numerical simulation of compressible turbulence accelerated by graphics processing unit: An open-source high accuracy accelerated computational fluid dynamic software, Phys. Fluids 34, 126106 (2022).
  164. F. De Vanna, F. Avanzi, M. Cogo, S. Sandrin, M. Bettencourt, F. Picano, and E. Benini, URANOS: A GPU accelerated Navier-Stokes solver for compressible wall-bounded flows, Comput. Phys. Commun. 287, 108717 (2023).
  165. K. Wang, S. Bose, and C. Ivey, GPU-accelrated full-wheel large-eddy simulations of a transonic fan stage, in Turbo Expo: Power for Land, Sea, and Air (ASME, New York, 2024), Vol. 88070, p. V12CT32A042.
  166. Y. Kim, D. Ghosh, E. M. Constantinescu, and R. Balakrishnan, GPU-accelerated DNS of compressible turbulent flows, Comput. Fluids 251, 105744 (2023).
  167. A. Ceci, A. Palumbo, J. Larsson, and S. Pirozzoli, On low-frequency unsteadiness in swept shock wave-boundary layer interactions, J. Fluid Mech. 956, R1 (2023).
  168. P. C. Boldini, R. Hirai, P. Costa, J. W. R. Peeters, and R. Pecnik, CUBENS: A GPU-accelerated high-order solver for wall-bounded flows with non-ideal fluids, Comput. Phys. Commun. 309, 109507 (2025).
  169. E. Slaughter, W. Lee, S. Treichler, M. Bauer, and A. Aiken, Regent: A high-productivity programming language for HPC with logical regions, in Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis (SC'15) (IEEE, Los Alamitos, CA, 2015), pp. 1–12.
  170. S. Pirozzoli, Generalized conservative approximations of split convective derivative operators, J. Comput. Phys. 229, 7180 (2010).
  171. J. Choi, Y. Kim, and H.-Y. Yeom, Overcoming GPU memory capacity limitations in hybrid MPI implementations of CFD, in Internet and Distributed Computing Systems, edited by R. Montella, A. Ciaramella, G. Fortino, A. Guerrieri, and A. Liotta (Springer International, Cham, 2019), pp. 100–111.
  172. J. Lai, H. Yu, Z. Tian, and H. Li, Hybrid MPI and CUDA parallelization for CFD applications on multi-GPU HPC clusters, Sci. Program. 2020, 8862123 (2020).
  173. M. Kurz, D. Kempf, M. P Blind, P. Kopper, P. Offenhäuser, A. Schwarz, S. Starr, J. Keim, and A. Beck, Galæxi: Solving complex compressible flows with high-order discontinuous Galerkin methods on accelerator-based systems, Comput. Phys. Commun. 306, 109388 (2025).
  174. D. A Bezgin, A. B. Buhendwa, and N. A. Adams, Jax-fluids 2.0: Towards HPC for differentiable CFD of compressible two-phase flows, Comput. Phys. Commun. 308, 109433 (2025).
  175. P. Grete, J. C. Dolence, J. M. Miller, J. Brown, B. Ryan, A. Gaspar, F. Glines, S. Swaminarayan, J. Lippuner, and C. Solomon, Parthenon—A performance portable block-structured adaptive mesh refinement framework, Int. J. High Perform. Comput. Appl. 37, 465 (2023).
  176. F. D. Witherden, A. M. Farrington, and P. E. Vincent, PyFR: An open source framework for solving advection–Diffusion type problems on streaming architectures using the flux reconstruction approach, Comput. Phys. Commun. 185, 3028 (2014).
  177. L. Jofre, A. M. A. Abdellatif, and G. Oyarzun Altamirano, RHEA: An open-source reproducible hybrid-architecture flow solver engineered for academia, J. Open Source Softw. 8, 4637 (2023).
  178. W. Xue, H. Wang, and C. J. Roy, CPU–GPU heterogeneous code acceleration of a finite volume computational fluid dynamics solver, Future Gener. Comput. Syst. 158, 367 (2024).
  179. F. Salvadore, G. Soldati, A. Ceci, G. Rossi, A. Memmolo, G. D. Posta, D. Modesti, S. Sathyanarayana, M. Bernardini, and S. Pirozzoli, STREAmS-2.1: Supersonic turbulent accelerated Navier-Stokes solver version 2.1, Comput. Phys. Commun. 314, 109652 (2025).
  180. F. De Vanna and G. Baldan, URANOS-2.0: Improved performance, enhanced portability, and model extension towards exascale computing of high-speed engineering flows, Comput. Phys. Commun. 303, 109285 (2024).
  181. J. Romero, J. Crabill, J. E. Watkins, F. D. Witherden, and A. Jameson, ZEFR: A GPU-accelerated high-order solver for compressible viscous flows using the flux reconstruction method, Comput. Phys. Commun. 250, 107169 (2020).
  182. M. Karp, R. Stanly, T. Mukha, L. Galimberti, S. Toosi, H. Song, L. Dalcin, S. Rezaeiravesh, N. Jansson, S. Markidis, M. Parsani, S. Bose, L. Sanjiva, and P. Schlatter, Effects of lower floating-point precision on scale-resolving numerical simulations of turbulence, J. Comput. Phys. 549, 114600 (2026).
  183. G. A. Bres, S. T. Bose, C. B. Ivey, M. Emory, and F. Ham, GPU-accelerated large-eddy simulations of supersonic jets from twin rectangular nozzle, in 28th AIAA/CEAS Aeroacoustics 2022 Conference (AIAA, Reston, VA, 2022), p. 3001.
  184. R. Saurel, F. Petitpas, and R. Abgrall, Modelling phase transition in metastable liquids: Application to cavitating and flashing flows, J. Fluid Mech. 607, 313 (2008).
  185. F. Petitpas, J. Massoni, R. Saurel, E. Lapebie, and L. Munier, Diffuse interface model for high speed cavitating underwater systems, Int. J. Multiph. Flow 35, 747 (2009).
  186. D. D. Joseph, J. Belanger, and G. S. Beavers, Breakup of a liquid drop suddenly exposed to a high-speed airstream, Int. J. Multiph. Flow 25, 1263 (1999).
  187. Q. Li, Y. Lv, and L. Fu, A high-order diffuse-interface method with TENO-THINC scheme for compressible multiphase flows, Int. J. Multiph. Flow 173, 104732 (2024).
  188. S. H. Bryngelson, K. Schmidmayer, V. Coralic, J. C. Meng, K. Maeda, and T. Colonius, MFC: An open-source high-order multi-component, multi-phase, and multi-scale compressible flow solver, Comput. Phys. Commun. 266, 107396 (2021).
  189. W. Zhang, A. Almgren, V. Beckner, J. Bell, J. Blaschke, Cy Chan, M. Day, B. Friesen, K. Gott, and G. Daniel, AMReX: A framework for block-structured adaptive mesh refinement, J. Open Source Softw. 4, 1370 (2019).
  190. W. Zhang, A. Myers, K. Gott, A. Almgren, and J. Bell, Amrex: Block-structured adaptive mesh refinement for multiphysics applications, Int. J. High Perform. Comput. Appl. 35, 508 (2021).
  191. A. Radhakrishnan, H. Le Berre, B. Wilfong, J.-S. Spratt, M. Rodriguez Jr., T. Colonius, and S. H. Bryngelson, Method for portable, scalable, and performant GPU-accelerated simulation of multiphase compressible flow, Comput. Phys. Commun. 302, 109238 (2024).
  192. S. Rao, B. Chen, and X. Xu, Heterogeneous CPU-GPU parallelization for modeling supersonic reacting flows with detailed chemical kinetics, Comput. Phys. Commun. 300, 109188 (2024).
  193. M. T. H. de Frahan, J. S. Rood, M. S. Day, H. Sitaraman, S. Yellapantula, B. A. Perry, R. W. Grout, A. Almgren, W. Zhang, J. B. Bell, and J. H. Chen, PeleC: An adaptive mesh refinement solver for compressible reacting flows, Int. J. High Perform. Comput. Appl. 37, 115 (2023).
  194. M. T. Henry de Frahan, L. Esclapez, J. Rood, N. T. Wimer, P. Mullowney, B. A. Perry, L. Owen, H. Sitaraman, S. Yellapantula, M. Hassanaly, M. J. Rahimi, M. J. Martin, O. A. Doronina, N. A. Sreejith, M. Rieth, W. Ge, R. Sankaran, A. S. Almgren, W. Zhang, J. B. Bell, et al., The Pele simulation suite for reacting flows at exascale, in Proceedings of the 2024 SIAM Conference on Parallel Processing for Scientific Computing (PP) (SIAM, Philedelphia, PA, 2024), pp. 13–25.
  195. H. Sitaraman, S. Yellapantula, M. T. H. de Frahan, B. Perry, J. Rood, R. Grout, and M. Day, Adaptive mesh based combustion simulations of direct fuel injection effects in a supersonic cavity flame-holder, Combust. Flame. 232, 111531 (2021).
  196. L. Placco, N. Cogo, M. Bernardini, A. Aboudan, F. Ferri, and F. Picano, Large-eddy simulation of the unsteady supersonic flow around a mars entry capsule at different angles of attack, Aerosp. Sci. Technol. 143, 108709 (2023).
  197. M. Cogo, D. Modesti, M. Bernardini, and F. Picano, DNS of supersonic turbulent boundary layers over rough surfaces, in APS DFD Meeting Abstracts (APS, New York, 2024), pp. X31–011.
  198. J. H. Chen, Petascale direct numerical simulation of turbulent combustion-fundamental insights towards predictive models, Proc. Combust. Inst. 33, 99 (2011).
  199. J. M. Levesque, R. Sankaran, and R. Grout, Hybridizing S3D into an exascale application using OpenACC: An approach for moving to multi-petaflops and beyond, in Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis (SC12) (IEEE, Los Alamitos, CA, 2012), pp. 1–11.
  200. Z.-M. Liao, L.-B. Chen, Z.-H. Wan, N.-S. Liu, and X.-Y. Lu, GPU acceleration of four-way coupled PP-DNS for compressible particle-laden wall turbulence, Int. J. Multiph. Flow 176, 104840 (2024).
  201. M. Xiao, A. Ceci, P. Costa, J. Larsson, and S. Pirozzoli, CaLES: A GPU-accelerated solver for large-eddy simulation of wall-bounded flows, Comput. Phys. Commun. 310, 109546 (2025).
  202. T. Zahtila, W. Lu, L. Chan, and A. Ooi, A systematic study of the grid requirements for a spectral element method solver, Comput. Fluids 251, 105745 (2023).
  203. Computational and Information Systems Laboratory, Derecho: HPE Cray E. X. System (University Community Computing), Technical Report, NSF National Center for Atmospheric Research, Boulder, CO (2023).
  204. Y. Ogura and N. A. Phillips, Scale analysis of deep and shallow convection in the atmosphere, J. Atmos. Sci. 19, 173 (1962).
  205. J. Schalkwijk, E. J. Griffith, F. H. Post, and H. J. J. Jonker, High-performance simulations of turbulent clouds on a desktop PC: Exploiting the GPU, Bull. Am Meteorol. Soc. 93, 307 (2012).
  206. J. Schalkwijk, H. J. J. Jonker, A. P. Siebesma, and E. Van Meijgaard, Weather forecasting using GPU-based large-dddy simulations, Bull. Am Meteorol. Soc. 96, 715 (2015).
  207. J. Schalkwijk, H. J. J. Jonker, A. P. Siebesma, and F. C. Bosveld, A year-long large-eddy simulatoin of the weather over Cabau: An overview, Mon. Weather Rev. 143, 828 (2015).
  208. C. C. van Heerwaarden, B. J. H. van Stratum, T. Heus, J. A. Gibbs, E. Fedorovich, and J. P. Mellado, MicroHH 1.0: A computational fluid dynamics code for direct numerical simulation and large-eddy simulation of atmospheric boundary layer flows, Geosci. Model Dev. 10, 3145 (2017).
  209. J. A. Sauer and E. Muñoz Esparza, The FastEddy resident-GPU accelerated large-eddy simulation framework: Model formulation, dynamical-core validation and performance benchmarks, J. Adv. Model. Earth Syst. 12, e2020MS002100 (2020).
  210. B. Maronga, M. Gryschka, R. Heinze, F. Hoffmann, F. Kanani-Sühring, M. Keck, K. Ketelsen, M. O. Letzel, M. Sühring, and S. Raasch, The parallelized large-eddy simulation model (PALM) version 4.0 for atmospheric and oceanic flows: Model formulation, recent developments, and future perspectives, Geosci. Model Dev. 8, 2515 (2015).
  211. J. Dennis, J. Sun, S. Voelz, G. Bryan, and D. Richter, A portable and efficient Lagrangian particle capability for idealized atmospheric phenomena, in Proceedings of the Platform for Advanced Scientific Computing Conference (PASC24) (ACM Press, New York, 2024), pp. 1–11.
  212. L. Esclapez, L. Soucasse, C. Jungbacker, F. Jansson, S. de Roode, P. Costa, G. van den Oord, and A. Sclocco, Accelerating the dutch atmospheric large-eddy simulation (DALES) model with OpenACC, in Proceedings of the 39th IEEE International Parallel &Distributed Processing Symposium (IPDPS'25) (IEEE, Los Alamitos, CA, 2025).
  213. C. C. Kiris, M. F. Barad, J. A. Housman, E. Sozer, C. Brehm, and S. Moini-Yekta, The LAVA computational fluid dynamics solver, in Proceedings of the 52nd AIAA Aerospace Sciences Meeting (AIAA, Reston, VA, 2014), p. 0070.
  214. C. C. Kiris, J. A. Housman, M. F. Barad, C. Brehm, E. Sozer, and S. Moini-Yekta, Computational framework for launch, ascent, and vehicle aerodynamics LAVA, Aerosp. Sci. Technol. 55, 189 (2016).
  215. N. Peters, RotLES: A Rotorcraft-based Lattice Boltzmann LES Code for Rapid Analysis and Design Space Exploration, Technical Report, National Aeronautics and Space Administration (2025).
  216. C. W. Jackson, D. Appelhans, J. M. Derlaga, and P. G. Buning, GPU implementation of the OVERFLOW CFD code, in AIAA SCITECH 2024 Forum (AIAA, Reston, VA, 2024), p. 0042.
  217. L. Placco, G. Soldati, M. Bernardini, and F. Picano, On flight instabilities of capsule-rigid parachute system during supersonic planetary descent, Aerosp. Sci. Technol. 160, 110026 (2025).
  218. S. C. Spiegel, D. A. Yoder, J. R. DeBonis, H. T. Huynh, G. Heinlein, M. R. Borghi, and N. J. Georgiadis, New capabilities and improvements to the high-order Glenn flux reconstruction code, in AIAA 2025-0061, Session: NASA's Revolutionary Computational Aerosciences, AIAA SCITECH 2025 Forum, Orlando, FL (AIAA, 2025).
  219. From supercomputers to wind tunnels: NASA road to Artemis II (2025), https://www.nasa.gov/directorates/esdmd/common-exploration-systems-development-division/space-launch-system/from-supercomputers-to-wind-tunnels-nasas-road-to-artemis-ii/.
  220. G. H. Bryan and J. M. Fritsch, A benchmark simulation for moist nonhydrostatic numerical models, Mon. Weather Rev. 130, 2917 (2002).
  221. T. Heus, C. C. van Heerwaarden, H. J. J. Jonker, A. P. Siebesma, S. Axelsen, K. Van Den Dries, O. Geoffroy, A. F. Moene, D. Pino, and S. R. De Roode, Formulation of the dutch atmospheric large-eddy simulation (DALES) and overview of its applications, Geosci. Model Dev. 3, 415 (2010).
  222. J. D. Albertson, Large eddy simulation of land-atmosphere interaction, Ph.D. thesis, University of California, Davis, 1996.
  223. M. T. Nguyen, P. Castonguay, and E. Laurendeau, GPU parallelization of multigrid RANS solver for three-dimensional aerodynamic simulations on multiblock grids, J. Supercomput. 75, 2562 (2019).
  224. M. Lee, N. Malaya, and R. D. Moser, Petascale direct numerical simulation of turbulent channel flow on up to 786k cores, in Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis (SC13) (IEEE, Los Alamitos, CA, 2013), pp. 1–11.
  225. M. Turisini, G. Amati, and M. Cestari, LEONARDO: A pan-European pre-exascale supercomputer for HPC and AI applications, arXiv:2307.16885.
  226. Z. Gong, G. Deng, C. An, Z. Wu, and X. Fu, A high order finite difference solver for simulations of turbidity currents with high parallel efficiency, Comput. Math. Appl. 128, 21 (2022).
  227. C. Canuto, M. Y. Hussaini, A. M. Quarteroni, and T. A. Zang, Spectral Methods in Fluid Dynamics (Springer-Verlag, Berlin, 1988).
  228. A. Roccon, A GPU-ready pseudo-spectral method for direct numerical simulations of multiphase turbulence, Proc. Comput. Sci. 240, 17 (2024).
  229. A. G. Chatterjee, M. K. Verma, A. Kumar, R. Samtaney, B. Hadri, and R. Khurram, Scaling of a fast fourier transform and a pseudo-spectral fluid solver up to 196608 cores, J. Parallel. Distr. Com. 113, 77 (2018).
  230. K. Czechowski, C. Battaglino, C. McClanahan, K. Iyer, P.-K. Yeung, and R. Vuduc, On the communication complexity of 3D FFTs and its implications for exascale, in Proceedings of the ACM International Conference on Supercomputing (ICS) (ACM Press, New York, 2012), pp. 205–214.
  231. L. Dalcin, M. Mortensen, and D. E. Keyes, Fast parallel multidimensional FFT using advanced MPI, J. Parallel. Distr. Com. 128, 137 (2019).
  232. D. Pekurovsky, P3DFFT: A framework for parallel computations of Fourier transforms in three dimensions, SIAM J. Comput. 34, C192 (2012).
  233. J. Romero, P. Costa, and M. Fatica, Distributed-memory simulations of turbulent flows on modern GPU systems using an adaptive pencil decomposition library, in Proceedings of the Platform for Advanced Scientific Computing Conference (PASC22) (ACM Press, New York, 2022), pp. 1–11.
  234. R. Uma-Vaideswaran, J. Romero, D. L. Dotson, D. Appelhans, and P. K. Yeung, A peak performance model for all-to-all on hierarchical systems and its applications, in Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis (SC25) (IEEE, Los Alamitos, CA, 2025), pp. 1442–1451.
  235. N. Okamoto, T. Ishihara, M. Yokokawa, and Y. Kaneda, Effects of finite arithmetic precision on large-scale direct numerical simulation of box turbulence by spectral method, Phys. Rev. Fluids 10, 064603 (2025).
  236. V. Sze, Y.-H. Chen, T.-J. Yang, and J. S. Emer, Efficient processing of deep neural networks: A tutorial and survey, Proc. IEEE 105, 2295 (2017).
  237. R. Sakamoto, M. Kondo, K. Fujita, T. Ichimura, and K. Nakajima, The effectiveness of low-precision floating arithmetic on numerical codes: A case study on power consumption, in Proceedings of the Supercomputing Asia and International Conference on High Performance Computing in Asia Pacific Region Workshops (ACM Press, New York, 2020), pp. 199–206.
  238. K. Kulkarni, S. Kemmler, A. Schwarz, G. Gedik, Y. Chen, D. Papageorgiou, I. Kavroulakis, and R. Iakymchuk, Harvesting energy consumption on european HPC systems: Sharing experience from the CEEC project (unpublished).
  239. Y. Arafa, A. ElWazir, A. ElKanishy, Y. Aly, A. Elsayed, A.-H. Badawy, G. Chennupati, S. Eidenbenz, and N. Santhi, Verified instruction-level energy consumption measurement for NVIDIA GPUs, in Proceedings of the 17th ACM International Conference on Computing Frontiers (ACM Press, New York, 2020), pp. 60–70.
  240. A. Kashi, H. Lu, W. Brewer, D. Rogers, M. Matheson, M. Shankar, and F. Wang, Mixed-precision numerics in scientific applications: Survey and perspectives, arXiv:2412.19322.
  241. A. Abdelfattah, H. Anzt, E. G. Boman, E. Carson, T. Cojean, J. Dongarra, A. Fox, M. Gates, N. J Higham, X. Li, et al., A survey of numerical linear algebra methods utilizing mixed-precision arithmetic, Int. J. High Perform. Comput. Appl. 35, 344 (2021).
  242. M. Bernardini, S. Pirozzoli, and P. Orlandi, Velocity statistics in turbulent channel flow up to Reτ=4000, J. Fluid Mech. 742, 171 (2014).
  243. B. Wilfong, A. Radhakrishnan, H. Le Berre, D. J. Vickers, T. Prathi, N. Tselepidis, B. Dorschner, R. Budiardja, B. Cornille, A. Abbott, F. Schäfer, and S. H. Bryngelson, Simulating many-engine spacecraft: Exceeding 1 quadrillion degrees of freedom via information geometric regularization, in Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis (SC25) (IEEE, Los Alamitos, CA, 2025), pp. 14–24.
  244. R. Vacondio, C. Altomare, M. De Leffe, X. Hu, D. Le Touzé, S. Lind, J.-C. Marongiu, S. Marrone, B. D. Rogers, and A. Souto-Iglesias, Grand challenges for smoothed particle hydrodynamics numerical schemes, Comput. Part. Mech. 8, 575 (2021).
  245. J. Pozorski and M. Olejnik, Smoothed particle hydrodynamics of multiphase flows: An overview, Acta Mech. 235, 1685 (2024).
  246. A. Tiribocchi, M. Durve, M. Lauricella, A. Montessori, J.-M. Tucny, and S. Succi, Lattice Boltzmann simulations for soft flowing matter, Phys. Rep. 1105, 1 (2025).
  247. J. Capecelatro and O. Desjardins, An Euler-Lagrange strategy for simulating particle-laden flows, J. Comput. Phys. 238, 1 (2013).
  248. D. Zwick and S. Balachandar, A scalable Euler–Lagrange approach for multiphase flow simulation on spectral elements, Int. J. High Perform. Comput. Appl. 34, 316 (2020).
  249. K. Zhai, T. Banerjee, D. Zwick, J. Hackl, and S. Ranka, Dynamic load balancing for compressible multiphase turbulence, in Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis (SC18) (IEEE, Los Alamitos, CA, 2018), pp. 318–327.
  250. P. Valero-Lara, F. D. Igual, M. Prieto-Matías, A. Pinelli, and J. Favier, Accelerating fluid–solid simulations (lattice-Boltzmann and immersed-boundary) on heterogeneous architectures, J. Comput. Sci. 10, 249 (2015).
  251. X. Zhang, F. Zonta, Z. F Tian, G. J. Nathan, R. C. Chin, and A. Soldati, Dynamics of semi-and neutrally-buoyant particles in thermally stratified turbulent channel flow, Int. J. Multiph. Flow 139, 103595 (2021).
  252. J. Sweet, D. H. Richter, and D. Thain, GPU acceleration of Eulerian–Lagrangian particle-laden turbulent flow simulations, Int. J. Multiph. Flow 99, 437 (2018).
  253. M. Uhlmann, An immersed boundary method with direct forcing for the simulation of particulate flows, J. Comput. Phys. 209, 448 (2005).
  254. S. O. Unverdi and G. Tryggvason, A front-tracking method for viscous, incompressible, multi-fluid flows, J. Comput. Phys. 100, 25 (1992).
  255. A. M. Roma, C. S. Peskin, and M. J. Berger, An adaptive version of the immersed boundary method, J. Comput. Phys. 153, 509 (1999).
  256. J. C. B. de Motta, P. Costa, J. J. Derksen, C. Peng, L.-P. Wang, W.-P. Breugem, J.-L. Estivalèzes, S. Vincent, E. Climent, and P. Fede, Assessment of numerical methods for fully resolved simulations of particle-laden turbulent flows, Comput. Fluids 179, 1 (2019).
  257. P. Karnakov, F. Wermelinger, M. Chatzimanolakis, S. Litvinov, and P. Koumoutsakos, A high performance computing framework for multiphase, turbulent flows on structured grids, in Proceedings of the Platform for Advanced Scientific Computing Conference (ACM Press, New York, 2019).
  258. M. Chatzimanolakis, P. Weber, F. Wermelinger, and P. Koumoutsakos, CubismAMR—AC library for distributed block-structured adaptive mesh refinement, arXiv:2206.07345.
  259. P. Hadjidoukas, D. Rossinelli, F. Wermelinger, J. Sukys, U. Rasthofer, C. Conti, B. Hejazialhosseini, and P. Koumoutsakos, High throughput simulations of two-phase flows on Blue Gene/Q, in Parallel Computing: On the Road to Exascale (IOS Press, Bristol, UK, 2016), pp. 767–776.
  260. E. Aulisa, S. Manservisi, R. Scardovelli, and S. Zaleski, Interface reconstruction with least-squares fit and split advection in three-dimensional Cartesian geometry, J. Comput. Phys. 225, 2301 (2007).
  261. R. Reddy and R. Banerjee, GPU accelerated VOF based multiphase flow solver and its application to sprays, Comput. Fluids 117, 287 (2015).
  262. S. Ii, K. Sugiyama, S. Takeuchi, S. Takagi, Y. Matsumoto, and F. Xiao, An interface capturing method with a continuous function: The thinc method with multi-dimensional reconstruction, J. Comput. Phys. 231, 2328 (2012).
  263. M. Griebel and P. Zaspel, A multi-gpu accelerated solver for the three-dimensional two-phase incompressible Navier-Stokes equations, Comput. Sci. Res. Dev. 25, 65 (2010).
  264. In standard level-set methods, the level-set function is defined to be a signed distance function calculated from the distance at the interface that separates the two fluids.
  265. J. Kelly, GPU-accelerated simulation of two-phase incompressible fluid flow using a level-set method for interface capturing, in ASME International Mechanical Engineering Congress & Exposition (IMECE09) (ASME, New York, 2009), Vol. 9, p. 2221.
  266. S. Fu, Z. Hao, W. Su, H. Zhang, and L. Wang, Level-set lattice Boltzmann method for interface-resolved simulations of immiscible two-phase flow, Phys. Rev. E 110, 045309 (2024).
  267. F. Gibou, R. Fedkiw, and S. Osher, A review of level-set methods and some recent applications, J. Comput. Phys. 353, 82 (2018).
  268. Y. Li, B. Zhou, and X. Hu, A two-grid method for level-set based topology optimization with GPU-acceleration, J. Comput. Appl. Math. 389, 113336 (2021).
  269. D. Reska and M. Kretowski, GPU-accelerated image segmentation based on level sets and multiple texture features, Multimedia Tools Appl. 80, 5087 (2021).
  270. D. Reska and M. Kretowski, GPU-accelerated lung CT segmentation based on level sets and texture analysis, Sci. Rep. 14, 1444 (2024).
  271. J. A. Sethian, A fast marching level set method for monotonically advancing fronts, Proc. Natl. Acad. Sci. USA 93, 1591 (1996).
  272. Y.-H. R. Tsai, L.-T. Cheng, S. Osher, and H.-K. Zhao, Fast sweeping algorithms for a class of Hamilton–Jacobi equations, SIAM J. Numer. Anal. 41, 673 (2003).
  273. H. Zhao, Parallel implementations of the fast sweeping method, J. Comput. Math. 25, 421, (2007).
  274. M. Detrixhe, F. Gibou, and C. Min, A parallel fast sweeping method for the Eikonal equation, J. Comput. Phys. 237, 46 (2013).
  275. A. Roccon, F. Zonta, and A. Soldati, Phase-field modeling of complex interface dynamics in drop-laden turbulence, Phys. Rev. Fluids 8, 090501 (2023).
  276. S. Mirjalili, C. B. Ivey, and A. Mani, A conservative diffuse interface method for two-phase flows with provable boundedness properties, J. Comput. Phys. 401, 109006 (2020).
  277. S. S. Jain, Accurate conservative phase-field method for simulation of two-phase flows, J. Comput. Phys. 469, 111529 (2022).
  278. J. Kwack, J. Tramm, C. Bertoni, Y. Ghadar, B. Homerding, E. Rangel, C. Knight, and S. Parker, Evaluation of performance portability of applications and mini-apps across AMD, Intel and nVidia GPUs, in Proceedings of the 2021 International Workshop on Performance, Portability & Productivity in HPC (P3HPC) (IEEE, Los Alamitos, CA, 2021), pp. 45–56.
  279. J. Dongarra, M. Gates, P. Luszczek, and S. Tomov, Translational process: Mathematical software perspective, J. Comput. Sci. 52, 101216 (2021).
  280. M. Lehmann, M. J. Krause, G. Amati, M. Sega, H. Harting, and S. Gekle, Accuracy and performance of the lattice-Boltzmann method with 64-bit, 32-bit, and customized 16-bit number formats, Phys. Rev. E 106, 015308 (2022).
  281. M. Karp, R. Stanly, H. Song, T. Mukha, L. Galimberti, S. Toosi, L. Dalcin, S. Rezaeirsavesh, M. Munsch, N. Jansson, S. Markidis, M. Parsani, S. T. Bose, S. K. Lele, and P. Schlatter, Sensitivity of numerical simulations of turbulence to lower floating-point precision, in Proceedings of the Summer Program 2022 of the Center Turbulence Research (Stanford University, Stanford, CA, 2024).
  282. H. Ootomo, K. Ozaki, and R. Yokota, DGEMM on integer matrix multiplication unit, Int. J. High Perform. Comput. Appl. 38, 297 (2024).
  283. H. Liu, J. Li, and Y. Wang, A pilot study on tunable precision emulation via automatic BLAS offloading, arXiv:2503.22875.
  284. A. Schwarz, A. Anders, C. Brower, H. Bayraktar, J. Gunnels, K. Clark, R. G. Xu, S. Rodriguez, S. Cayrols, P. Tabaszewski, et al., Guaranteed DGEMM accuracy while using reduced precision tensor cores through extensions of the Ozaki scheme, in Proceedings of the Supercomputing Asia and International Conference on High Performance Computing in Asia Pacific Region Workshops (ACM Press, New York, 2026), pp. 91–101.
  285. P. Koumoutsakos, On roads less between AI and computational science, Nat. Rev. Phys. 6, 342 (2024).
  286. R. Vinuesa and S. L. Brunton, Enhancing computational fluid dynamics with machine learning, Nat. Comput. Sci. 2, 358 (2022).
  287. M. Curcic, A parallel Fortran framework for neural networks and deep learning, in Proceedings of the ACM SIGPLAN Fortran Forum (ACM Press, New York, 2019), Vol. 38, pp. 4–21.
  288. A. Sebastian, M. Le Gallo, R. Khaddam-Aljameh, and E. Eleftheriou, Memory devices and applications for in-memory computing, Nat. Nanotechnol. 15, 529 (2020).
  289. Z. Sun, S. Kvatinsky, X. Si, A. Mehonic, Y. Cai, and R. Huang, A full spectrum of computing-in-memory technologies, Nat. Electron. 6, 823 (2023).
  290. https://github.com/aroccon/GPU_DNS_LES_codes.git.

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation