Skip to main content
SpringerLink
Log in

Improvement of lattice Boltzmann methods based on gated recurrent unit neural network

  • Original Paper
  • Published:
Signal, Image and Video Processing Aims and scope Submit manuscript

Abstract

Compared with traditional computational fluid dynamics methods, the lattice Boltzmann method (LBM) has the advantages of simple program structure, adaptability to complex boundaries, and easy parallel computation. However, since LBM is an explicit algorithm, there are many iterations in the computation process, which leads to an increase in computation time. In this paper, we improve LBM based on deep learning by combining a convolutional neural network (CNN) and a gated recurrent unit neural network (GRU). Based on previous test data, the CNN module extracts spatial features during the computation, while the GRU processes the corresponding temporal features. Compared with the conventional LBM, this method can significantly reduce the computation time and improve the computational efficiency with guaranteed low Reynolds numbers of 1000 and 2000. At the high Reynolds number of 4000, the prediction error of the proposed method is increasing but still has a better performance. In order to verify the effectiveness and accuracy of the proposed algorithm, an eddying model widely used in the computational fluid field is developed. The proposed method not only has impressive results but also deals with non-stationary processes and steady-state problems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Data availability

The datasets generated during and/or analyzed during the current study are not publicly available since the data still have value for continued research but are available from the corresponding author on reasonable request.

References

  1. Lallemand, P., Luo, L.-S., Krafczyk, M., Yong, W.-A.: The lattice Boltzmann method for nearly incompressible flows. J. Comput. Phys. 431, 109713 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  2. Aidun, C.K., Clausen, J.R.: Lattice-Boltzmann method for complex flows. Ann. Rev. Fluid Mech. 42, 439–472 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  3. Samanta, R., Chattopadhyay, H., Guha, C.: A review on the application of lattice Boltzmann method for melting and solidification problems. Comput. Mater. Sci. 206, 111288 (2022)

    Article  Google Scholar 

  4. Lobovský, L., Vimmr, J.: Smoothed particle hydrodynamics and finite volume modelling of incompressible fluid flow. Math. Comput. Simul. 76(1), 124–131 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  5. Barad, M., Kocheemoolayil, J., Kiris, C.: Lattice Boltzmann and Navier-stokes cartesian cfd approaches for airframe noise predictions (2017)

  6. Haussmann, M., Ries, F., Jeppener-Haltenhoff, J.B., Li, Y., Schmidt, M., Welch, C., Illmann, L., Böhm, B., Nirschl, H., Krause, M.J., Sadiki, A.: Evaluation of a near-wall-modeled large eddy lattice Boltzmann method for the analysis of complex flows relevant to IC engines. Computation 8, 43 (2020)

    Article  Google Scholar 

  7. Krause, M.J., Kummerländer, A., Avis, S.J., Kusumaatmaja, H., Dapelo, D., Klemens, F., Gaedtke, M., Hafen, N., Mink, A., Trunk, R., Marquardt, J.E., Maier, M.-L., Haussmann, M., Simonis, S.: Openlb-open source lattice Boltzmann code. Comput. Math. Appl. 81, 258–288 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  8. Lohner, R.: Towards overcoming the LES crisis. Int. J. Comput. Fluid Dyn. 33, 1–11 (2019)

    Article  MathSciNet  Google Scholar 

  9. Hou, S., Sterling, J.D., Chen, S., Doolen, G.D.: A lattice Boltzmann subgrid model for high reynolds number flows. arXiv: Cellular Automata and Lattice Gases (1994)

  10. Dong, Y.-H., Sagaut, P., Marié, S.: Inertial consistent subgrid model for large-eddy simulation based on the lattice Boltzmann method. Phys. Fluids 20, 035104 (2008)

    Article  MATH  Google Scholar 

  11. Li, C., Zhao, Y., Ai, D., Wang, Q., Peng, Z., Li, Y.: Multi-component LBM-LES model of the air and methane flow in tunnels and its validation. Phys. A Stat. Mech. Appl. 553, 124279 (2020)

    Article  Google Scholar 

  12. Premnath, K.N., Pattison, M.J., Banerjee, S.: Dynamic subgrid scale modeling of turbulent flows using lattice-Boltzmann method. Phys. A Stat. Mech. Appl. 388(13), 2640–2658 (2009)

    Article  Google Scholar 

  13. Weickert, M., Teike, G., Schmidt, O., Sommerfeld, M.: Investigation of the les wale turbulence model within the lattice Boltzmann framework. Comput. Math. Appl. 59(7), 2200–2214 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  14. Malaspinas, O., Sagaut, P.: Consistent subgrid scale modelling for lattice Boltzmann methods. J. Fluid Mech. 700, 514 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  15. Sagaut, P.: Toward advanced subgrid models for lattice-Boltzmann-based large-eddy simulation: theoretical formulations. Comput. Math. Appl. 59(7), 2194–2199 (2010)

  16. Malaspinas, O., Sagaut, P.: Advanced large-eddy simulation for lattice Boltzmann methods: the approximate deconvolution model. Phys. Fluids 23, 105103 (2011)

  17. Marié, S., Gloerfelt, X.: Adaptive filtering for the lattice Boltzmann method. J. Comput. Phys. 333, 212–226 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  18. Nathen, P., Haussmann, M., Krause, M., Adams, N.: Adaptive filtering for the simulation of turbulent flows with lattice Boltzmann methods. Comput. Fluids 172, 510–523 (2018)

  19. Jacob, J., Malaspinas, O., Sagaut, P.: A new hybrid recursive regularised Bhatnagar-Gross-Krook collision model for lattice Boltzmann method-based large eddy simulation. J. Turbul. 19, 1–26 (2018)

    Article  MathSciNet  Google Scholar 

  20. Pruett, C.: Temporal large-eddy simulation: theory and implementation. Theor. Comput. Fluid Dyn. 22, 275–304 (2008)

    Article  MATH  Google Scholar 

  21. Zhang, D., Luo, Y., Zhao, Y., Li, Y., Mei, N., Yuan, H.: LBM-PFM simulation of directional frozen crystallisation of seawater in the presence of a single bubble. Desalination 542, 116065 (2022)

    Article  Google Scholar 

  22. Oberle, D., Pruett, C., Jenny, P.: Temporal large-eddy simulation based on direct deconvolution. Phys. Fluids 32, 065112 (2020)

    Article  Google Scholar 

  23. Yang, D., Karimi, H.R., Sun, K.: Residual wide-kernel deep convolutional auto-encoder for intelligent rotating machinery fault diagnosis with limited samples. Neural Netw. 141, 133–144 (2021)

    Article  Google Scholar 

  24. D’Humières, D., Ginzburg, I., Krafczyk, M., Lallemand, P., Luo, L.-S.: Multiple-relaxation-time lattice Boltzmann models in three dimensions. Philos. Trans. Ser. A Math. Phys. Eng. Sci. 360, 437–51 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  25. Dey, S., Mahato, R., Ali, S.: Linear stability of sand waves sheared by a turbulent flow. Environ. Fluid Mech. 22, 429 (2022)

    Article  Google Scholar 

  26. Haussmann, M., Simonis, S., Nirschl, H., Krause, M.: Direct numerical simulation of decaying homogeneous isotropic turbulence - numerical experiments on stability, consistency and accuracy of distinct lattice Boltzmann methods. Int. J. Mod. Phys. C 30, 1950074 (2019)

    Article  MathSciNet  Google Scholar 

  27. Geurts, B.: A framework for predicting accuracy limitations in large-eddy simulation. Phys. Fluids 14, L41 (2002)

    Article  MATH  Google Scholar 

  28. Meng, F., Karimi, H.: Emerging methodologies in stability and optimization problems of learning-based nonlinear model predictive control: A survey. Int. J. Circuit Theory Appl. 50, 4146 (2022)

    Article  Google Scholar 

  29. Chen, X., Yang, G., Yao, Q., Nie, Z., Jiang, Z.: A compressed lattice Boltzmann method based on ConvLSTM and ResNet. Comput. Math. Appl. 97, 162–174 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  30. Lei, Y., Karimi, H.R., Chen, X.: A novel self-supervised deep LSTM network for industrial temperature prediction in aluminum processes application. Neurocomputing 502, 177–185 (2022)

    Article  Google Scholar 

  31. Wu, C., Kinnas, S.A.: Parallel implementation of a viscous vorticity equation (visve) method in 3-d laminar flow. J. Comput. Phys. 426, 109912 (2021)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Funding

This work was supported by a grant from the National Natural Science Foundation of China (No. U2006228, 52171313).

Author information

Authors and Affiliations

  1. Department of System Science, University of Shanghai for Science and Technology, Shanghai, 200093, China

    Yuchen Zhao, Fei Meng & Xingtong Lu

Authors
  1. Yuchen Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fei Meng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xingtong Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

YZ wrote the main manuscript text and did the related experiments. FM prepared Figures 1, 2 and provided guidance on text ideas. XL revised and touched up the paper. All authors have read the manuscript

Corresponding author

Correspondence to Fei Meng.

Ethics declarations

Conflict of interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhao, Y., Meng, F. & Lu, X. Improvement of lattice Boltzmann methods based on gated recurrent unit neural network. SIViP 17, 3283–3291 (2023). https://doi.org/10.1007/s11760-023-02543-w

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11760-023-02543-w

Keywords

Search

Navigation