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Le, T.;  Kang, H.;  Kim, H. Computational Fluid Dynamics Simulations. Encyclopedia. Available online: https://encyclopedia.pub/entry/31129 (accessed on 27 July 2024).
Le T,  Kang H,  Kim H. Computational Fluid Dynamics Simulations. Encyclopedia. Available at: https://encyclopedia.pub/entry/31129. Accessed July 27, 2024.
Le, Thi-Thu-Huong, Hyoeun Kang, Howon Kim. "Computational Fluid Dynamics Simulations" Encyclopedia, https://encyclopedia.pub/entry/31129 (accessed July 27, 2024).
Le, T.,  Kang, H., & Kim, H. (2022, October 25). Computational Fluid Dynamics Simulations. In Encyclopedia. https://encyclopedia.pub/entry/31129
Le, Thi-Thu-Huong, et al. "Computational Fluid Dynamics Simulations." Encyclopedia. Web. 25 October, 2022.
Computational Fluid Dynamics Simulations
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This entry is adapted from the peer-reviewed paper 10.3390/su141911996

Computational fluid dynamics (CFD) simulations are employed in several fields, such as mechanical engineering, medicine, and civil engineering. CFD solvers are numerical tools for simulating fluid flow characteristics to design, analyze, or optimize fluid flow behavior.

CFD (computational fluid dynamics) laminar flow Naiver–Stokes equation

1. Introduction

Computational fluid dynamics (CFD) simulations are employed in several fields, such as mechanical engineering, medicine, and civil engineering. CFD solvers are numerical tools for simulating fluid flow characteristics to design, analyze, or optimize fluid flow behavior. However, high temporal and spatial resolution is required to achieve high accuracy in state-of-the-art CFD simulations. These solvers require expensive computational resources, especially with iterative problems. To this end, data-driven machine learning models not only estimate accurate approximation fluid flow fields, but also require fewer computational resources [1]. To reduce computational costs, a trained neural network (NN) might take the role of a portion of the numerical resolution process. As an illustration, several NN applications have been produced to solve and predict flow in terms of the large eddy simulation (LES) [2] and Reynolds-averaged Navier–Stokes (RANS) computations [3][4].
CFD simulations’ complexity might be reduced by using reduced order model (ROM) techniques, such as simplified physics methods, reduced basis (RB), or proper orthogonal decomposition (POD). In particular, deep learning (DL)-enabled ROM can be used to set up a nonlinear relationship between various inputs and outputs of a target system. The DL-enabled ROM, along with the training model, can generate a low-dimensional subspace that records the average behavior of flows. Through this training process, complex features that cannot be expressed explicitly in a functional form can be represented [5]. In practice, the DL-enabled ROM accurately captures fluid flow’s temporal and spatial nonlinear features. For example, Wang et al. [6] presented a model recognition of reduced-order fluid dynamic systems by DL. The researchers proved that their framework could capture complex fluid dynamics features with less computational cost. Furthermore, Fukami et al. [7] performed a super-resolution analysis of evidently under-resolved turbulent flow data based on the DL model and then reconstructed the high-resolution flow field. This successful model built a nonlinear mapping between low and high resolutions of the turbulent flow fields.
The various proposed DL-ROM algorithms [8][9] were evaluated on both linear and nonlinear time-dependent parameters to demonstrate the flexibility of this methodology and its incredible computing savings. After executing a prior dimensional reduction by POD, Fresca et al. [10] suggested that DL-based ROMs rely on DNNs, significantly reducing their training times. The blood flow in a cerebral aneurysm, the fluid-structure interaction between an elastic beam attached to a fixed, rigid block, and the flow around a cylindrical benchmark are all accurately predicted by the resulting POD-DL-ROMs in almost real-time. A novel DL framework called DL-ROM was also developed by Pant et al. [11] to build a neural network that can make non-linear projections to lower-order states. They then employ a 3D autoencoder and 3D U-Net-based architectures to effectively forecast future time steps of the simulation using the learned reduced state. By traversing time in the learned reduced state, their model DL-ROM can efficiently anticipate future time steps by building highly accurate reconstructions from the learned ROM. Recently, Kang et al. [12] presented POD-ROM, which quickly and precisely describes the flow status of the fluid field in rod bundles.
DL-based CFD models have recently attracted the attention of fluid flow and thermal engineering research as a reduced-order modeling method. To learn the solutions of parametric partial differential equations (PDEs) over irregular domains, including Navier–Stokes and heat transfer equations, Gao et al. [13] presented a physics-constrained convolutional neural network (CNN) architecture. Their findings showed how well the DL technique predicted temperature and velocity fields. The DL-based CFD model was employed by San et al. [14] to precisely resolve the spatial–temporal nonlinear characteristic in a fluid dynamic system. In addition, a data-driven DL model was also used by Sekar et al. [15] to measure laminar flow on an airfoil dataset. The experimental findings demonstrated that the model accurately predicted laminar flow fields using the airfoil geometry, Reynolds number, and attack angles as learning parameters. Jin et al. [16] subsequently suggested a CFD approach based on DL that directly maps the relationship between the pressure and velocity distribution on the surface of a cylinder to determine the fluctuating velocity field around it. The aforementioned studies proved and validated the capacity of DL-based CFD to offer substitute numerical solutions to physical issues.
Guo et al. [17] and Ribeiro et al. [18] are representative pioneers of DL-based CFD model approaches. The researchers used CNN and U-Net models to evaluate the proposed methods to predict steady flow around obstacles and different loss types.

2. Computational Fluid Dynamics Simulations

Recent advances in ML have impacted CFD research owing to its significant advantages. ML models estimate approximate thermal or fluid flow fields with low cost and accuracy compared with conventional CFD simulations. Sarghini et al. [19] developed ML model to estimate steady-state velocity flows. Next, Lee et al. [20] built an NN to predict unsteady flow around a cylinder. The researchers minimized the physical loss function comprising conservation laws and regression errors. Kashefi et al. [21] created an artificial neural network with modest geometry alterations to achieve various velocity and pressure fields. Furthermore, additional recent publications have demonstrated a variety of effective uses for CFD-based DL models, including physics-informed NN [3], airfoil design optimization [22], and acceleration of sparse linear system solutions [23][24].
The modern DL technique has recently played a vital role in CFD simulations. Deep neural network models have been used as data-driven surrogate models that efficiently approximate the velocity and pressure fields. Regarding the DL-based CFD approach, the direct estimation of fluid flow fields comprises two representative models: CNN-based CFD and variant autoencoder (AE)-based CFD.
In terms of a CNN-based CFD prediction approach, Guo et al. [17] proposed a CNN model for predicting stationary flow fields around solid objects. Moreover, previous studies [25][26] have used CNN models to learn arbitrary geometry representations. Georgiou et al. [27] developed a CNN application for reconstructing fluid force and flow prediction. Jin et al. [16] proposed a fusion CNN model to predict velocity snapshots around a cylinder. Furthermore, Zhang et al. [28] predicted the lift and drag coefficients of 2D airfoils using a CNN model. In addition, the CNN model was applied to measure flow in arbitrary shapes by Viquerat et al. [29].
In terms of AE and its variant U-Net model-based CFD prediction approach, AE models were used for supervised learning to predict various full-field flows in [16][17][20]. Especially among the various AE architectures, the U-Net model was recently applied successfully to estimate CFD flows. According to Ronneberger et al. [30], U-Net models might achieve the best segmentation accuracy by fusing high-level latent-space representation with low-level characteristics. Thuerey et al. [31] applied the U-Net model to estimate turbulent flow around airfoils, including the velocity and pressure flows, which were computed using RANS. Fukami at el. [7] applied the U-Net model to reconstruct turbulence with remarkable accuracy from rough flow field images. A recurrent U-Net architecture was investigated and developed by Kamrava et al. [32] to predict stationary velocity and pressure fields in porous membranes. Wang at el. [33] proposed a gated U-Net-based pixel CNN++ architecture to simulate fluids in porous media. Ribeiro et al. [18] applied the high-performance accuracy of the U-Net model to steady-state laminar flow approximation around simple obstacles. Chen et al. [34] proposed a twin-decoder based on the U-Net model to reconstruct incompressible laminar flow on 2D obstacle data.
In addition, the flow field feature information is crucial for enhancing the performance accuracy of flow estimation models. For example, Ribeiro et al. [18] and Alvaro et al. [32] reported remarkable prediction results through deep CFD models to predict the velocities and pressure by generating features based on the signed distance function (SDF) and flow region channel. Peng et al. [35] generated network input learning using the SDF and temperature field from numerical simulation data as output learning to feed the CNN model. SDF and binary features were developed for CFD input learning of CNN and U-Net models in [36]. Li et al. [37] proposed a wall distance field and space coordinate field for the U-Net model’s input features.

References

  1. Portwood, G.D.; Mitra, P.P.; Ribeiro, M.D.; Nguyen, T.M.; Nadiga, B.T.; Saenz, J.A.; Chertkov, M.; Garg, A.; Anandkumar, A.; Dengel, A.; et al. Turbulence Forecasting via Neural Ode. 2019. Available online: https://arxiv.org/abs/1911.05180 (accessed on 22 February 2022).
  2. Beck, A.D.; Flad, D.G.; Munz, C. Deep neural networks for data-driven turbulence models. CoRR 2018, abs/1806.04482. Available online: http://arxiv.org/abs/1806.04482 (accessed on 25 February 2022).
  3. Ling, J.; Kurzawski, A.; Templeton, J. Reynolds averaged turbulence modelling using deep neural networks with embedded invariance. J. Fluid Mech. 2016, 807, 155–166.
  4. Tracey, B.D.; Duraisamy, K.; Alonso, J.J. A machine learning strategy to assist turbulence model development. In Proceedings of the 53rd AIAA Aerospace Sciences Meeting, Kissimmee, FL, USA, 5–9 January 2015.
  5. Hagan, M.T.; Demuth, H.B.; Beale, M.H.; Jesús, O.D. Neural Network Design; PWS Publishing Co.: Cambridge, MA, USA, 2014.
  6. Wang, Z.; Xiao, D.; Fang, F.; Govindan, R.; Pain, C.C.; Guo, Y. Model identification of reduced order fluid dynamics systems using deep learning. Int. Numer. Methods Fluids 2017, 86, 255–268.
  7. Fukami, K.; Fukagata, K.; Taira, K. Superresolution reconstruction of turbulent flows with machine learning. J. Fluid Mech. 2019, 870, 106–120.
  8. Fresca, S.; Dedè, L.; Manzoni, A. A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. J. Sci. Comput. 2021, 87, 61.
  9. Fresca, S.; Manzoni, A. POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Comput. Methods Appl. Mech. Eng. 2022, 388, 114181.
  10. Fresca, S.; Manzoni, A. Real-Time Simulation of Parameter-Dependent Fluid Flows through Deep Learning-Based Reduced Order Models. Fluids 2021, 6, 259.
  11. Pant, P.; Doshi, R.; Bahl, P.; Barati, F.A. Deep learning for reduced order modelling and efficient temporal evolution of fluid simulations. Phys. Fluids 2021, 33, 107101.
  12. Kang, H.; Tian, Z.; Chen, G.; Li, L.; Wang, T. Application of POD reduced-order algorithm on data-driven modeling of rod bundle. Nucl. Eng. Technol. 2022, 54, 36–48.
  13. Gao, H.; Sun, L.; Wang, J.-X. Phygeonet: Physicsinformed geometry-adaptive convolutional neural networks for solving parametric pdes on irregular domain. J. Comput. Phys. 2021, 428, 110079.
  14. San, O.; Maulik, R.; Ahmed, M. An artificial neural network framework for reduced order modeling of transient flows. Commun. Nonlinear Sci. Numer. Simul. 2019, 77, 271–287. Available online: https://www.sciencedirect.com/science/article/pii/S1007570419301364 (accessed on 18 March 2022).
  15. Sekar, V.; Khoo, B.C. Fast flow field prediction over airfoils using deep learning approach. Phys. Fluids 2019, 31, 057103.
  16. Jin, X.; Cheng, P.; Chen, W.-L.; Li, H. Prediction model of velocity field around circular cylinder over various Reynolds numbers by fusion convolutional neural networks based on pressure on the cylinder. Phys. Fluids 2018, 30, 047105.
  17. Guo, X.; Li, W.; Iorio, F. Convolutional Neural Networks for Steady Flow Approximation; ser. KDD ’16; Association for Computing Machinery: New York, NY, USA, 2016; pp. 481–490.
  18. Ribeiro, M.D.; Rehman, A.; Ahmed, S.; Dengel, A. Deepcfd: Efficient Steady-State Laminar Flow Approximation with Deep Convolutional Neural Networks. 2020. Available online: https://arxiv.org/abs/2004.08826 (accessed on 13 March 2022).
  19. Sarghini, F.; de Felice, G.; Santini, S. Neural networks based subgrid scale modeling in large eddy simulations. Comput. Fluids 2003, 32, 97–108. Available online: https://www.sciencedirect.com/science/article/pii/S0045793001000986 (accessed on 16 March 2022).
  20. Lee, S.; You, D. Data-driven prediction of unsteady flow over a circular cylinder using deep learning. J. Fluid Mech. 2019, 879, 217–254.
  21. Kashefi, A.; Rempe, D.; Guibas, L.J. A point-cloud deep learning framework for prediction of fluid flow fields on irregular geometries. Phys. Fluids 2021, 33, 027104.
  22. Lui, H.F.S.; Wolf, W.R. Construction of reducedorder models for fluid flows using deep feedforward neural networks. J. Fluid Mech. 2019, 872, 963–994.
  23. Tompson, J.; Schlachter, K.; Sprechmann, P.; Perlin, K. Accelerating Eulerian Fluid Simulation with Convolutional Networks. 2016. Available online: https://arxiv.org/abs/1607.03597 (accessed on 28 March 2022).
  24. Ribeiro, M.D.; Portwood, G.D.; Mitra, P.; Nyugen, T.M.; Nadiga, B.T.; Chertkov, M.; Anandkumar, A.; Schmidt, D.P.; Team, N.; Team, U.; et al. A data-driven approach to modeling turbulent decay at non-asymptotic Reynolds numbers. In Proceedings of the APS Division of Fluid Dynamics Meeting Abstracts 2019, Provided by the SAO/NASA Astrophysics Data System, Seattle, WA, USA, 23–26 November 2019; p. G16.002.
  25. Gupta, S.; Girshick, R.; Arbeláez, P.; Malik, J. Learning Rich Features from Rgb-D Images for Object Detection and Segmentation. 2014. Available online: https://arxiv.org/abs/1407.5736 (accessed on 27 March 2022).
  26. Socher, R.; Huval, B.; Bhat, B.; Manning, C.D.; Ng, A.Y. Convolutional-recursive deep learning for 3d object classification. In Proceedings of the 25th International Conference on Neural Information Processing Systems, Harrahs and Harveys, NV, USA, 3–8 December 2012; ser. NIPS’12. Curran Associates Inc.: Red Hook, NY, USA, 2012; Volume 1, pp. 656–664.
  27. Georgiou, T.; Schmitt, S.; Olhofer, M.; Liu, Y.; Bäck, T.; Lew, M. Learning fluid flows. In Proceedings of the 2018 International Joint Conference on Neural Networks (IJCNN), Rio de Janeiro, Brazil, 8–13 July 2018; pp. 1–8.
  28. Zhang, Y.; Sung, W.-J.; Mavris, D. Application of Convolutional Neural Network to Predict Airfoil Lift coefficient. 2017. Available online: https://arxiv.org/abs/1712.10082 (accessed on 16 March 2022).
  29. Viquerat, J.; Hachem, E. A supervised neural 10 VOLUME, 2021Author Le et al.: Towards Incompressible Laminar Flow Estimation Based on Interpolated Feature Generation and Deep Learning network for drag prediction of arbitrary 2d shapes in laminar flows at low reynolds number. Comput. Fluids 2020, 210, 104645. Available online: https://www.sciencedirect.com/science/article/pii/S0045793020302164 (accessed on 2 April 2022).
  30. Ronneberger, O.; Fischer, P.; Brox, T. Unet: Convolutional Networks for Biomedical Image Segmentation. 2015. Available online: https://arxiv.org/abs/1505.04597 (accessed on 4 April 2022).
  31. Thuerey, N.; Weißenow, K.; Prantl, L.; Hu, X. Deep learning methods for reynolds-averaged navier–stokes simulations of airfoil flows. AIAA J. 2020, 58, 25–36.
  32. Kamrava, S.; Tahmasebi, P.; Sahimi, M. Physics and image-based prediction of fluid flow and transport in complex porous membranes and materials by deep learning. J. Membr. Sci. 2021, 622, 119050.
  33. Wang, Y.D.; Chung, T.; Armstrong, R.T.; Mostaghimi, P. Ml-lbm: Machine Learning Aided Flow Simulation in Porous Media. 2020. Available online: https://arxiv.org/abs/2004.11675 (accessed on 5 March 2022).
  34. Chen, J.; Viquerat, J.; Heymes, F.; Hachem, E. A Twin-Decoder Structure for Incompressible Laminar Flow Reconstruction with Uncertainty Estimation around 2D Obstacles. 2021. Available online: https://arxiv.org/abs/2104.03619 (accessed on 7 April 2022).
  35. Peng, J.-Z.; Liu, X.; Aubry, N.; Chen, Z.; Wu, W.-T. Data-driven modeling of geometryadaptive steady heat conduction based on convolutional neural networks. Case Stud. Thermal Eng. 2021, 28, 101651. Available online: https://www.sciencedirect.com/science/article/pii/S2214157X21008145 (accessed on 10 April 2022).
  36. Eichinger, M.; Heinlein, A.; Klawonn, A. Stationary flow predictions using convolutional neural networks. In ENUMATH, Lecture Notes in Computational Science and Engineering; Springer: Berlin/Heidelberg, Germany, 2019; Volume 139.
  37. Li, K.; Li, H.; Li, S.; Chen, Z. Fully convolutional neural network prediction method for aerostatic performance of bluff bodies based on consistent shape description. Appl. Sci. 2022, 12, 3147.
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Howon Kim
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