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Multi-GPU accelerated cellular automaton model for simulating the solidification structure of continuous casting bloom

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Abstract

The continuous casting bloom is characterized by a large size and long process, leading to tremendous calculation. It takes a long time to simulate the solidification structure by the traditional sequential algorithm on the CPU which cannot satisfy the industrial demand for guiding the process. This study developed a multi-GPU-based cellular automaton model to accelerate the calculation. Firstly, a heterogeneous GPU-CA parallel algorithm was developed to optimize the calculation parallelism by eliminating the data dependency and data race among cells, where the capture process adopted a random-principle-based arbitration mechanism to determine which neighbor obtains the final capture right. Then, the multi-stream communication scheme was developed to overlap the calculation of the inner region and the data transferring and calculation of the halo region, hiding the overhead of data exchange between GPUs. Finally, the present model was validated by the analytical LGK model value, and it was applied to simulate the solidification structure of GCr15 in a certain steel plant. The simulation result shows a clear solidification structure with different crystal zone of columnar, equiaxed, and where the columnar transfers into equiaxed (CET). The proportion of crystal zone agrees well with the low-power images from field experiments with relative errors of 0.032%, 0.013%, and 0.025%. Also, the multi-GPU application can calculate the temperature distribution during the solidification process with the maximum relative error of 0.013% compared to the field data. Furthermore, in the case of owning the almost same calculation precision as a single-core CPU, the speedup of the present model is up to 700x, whereas the speedup of the CPU with 20 cores is only about 14.2x.

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References

  1. Zhao P, Heinrich JC (2001) Front-tracking finite element method for dendritic solidification. J Comput Phys 173:765–796. https://doi.org/10.1006/jcph.2001.6911

    Article  MATH  Google Scholar 

  2. Merle R, Dolbow J (2002) Solving thermal and phase change problems with the eXtended finite element method. Comput Mech 28:339–350. https://doi.org/10.1007/s00466-002-0298-y

    Article  MATH  Google Scholar 

  3. Kim YT, Goldenfeld N, Dantzig J (2000) Computation of dendritic microstructures using a level set method. Phys Rev E 62:2471–2474. https://doi.org/10.1103/PhysRevE.62.2471

    Article  Google Scholar 

  4. Osher S, Fedkiw RP (2001) Level set methods: an overview and some recent results. J Comput Phys 169:463–502. https://doi.org/10.1006/jcph.2000.6636

    Article  MathSciNet  MATH  Google Scholar 

  5. Takaki T, Ohno M, Shimokawabe T, Aoki T (2014) Two-dimensional phase-field simulations of dendrite competitive growth during the directional solidification of a binary alloy bicrystal. Acta Mater 81:272–283. https://doi.org/10.1016/j.actamat.2014.08.035

    Article  Google Scholar 

  6. Tonks MR, Aagesen LK (2019) The phase field method: mesoscale simulation aiding material discovery. Annu Rev Mater Res 49:79–102. https://doi.org/10.1146/annurev-matsci-070218-010151

    Article  Google Scholar 

  7. Luo S, Wang WL, Zhu MY (2018) Cellular automaton modeling of dendritic growth of Fe-C binary alloy with thermosolutal convection. Int J Heat Mass Tran 116:940–950. https://doi.org/10.1016/j.ijheatmasstransfer.2017.09.074

    Article  Google Scholar 

  8. Zhu MF, Dai T, Lee SY, Hong CP (2008) Modeling of solutal dendritic growth with melt convection. Comput Math Appl 55:1620–1628. https://doi.org/10.1016/j.camwa.2007.08.023

    Article  MathSciNet  MATH  Google Scholar 

  9. Wang WL, Ji C, Luo S, Zhu MY (2018) Modeling of dendritic evolution of continuously cast steel billet with cellular automaton. Metall Mater Trans B 49:200–212. https://doi.org/10.1007/s11663-017-1131-5

    Article  Google Scholar 

  10. Wei LX, Wang M, Huang WD (2012) Orientation selection of equiaxed dendritic growth by three-dimensional cellular automaton model. Physica B 407:2471–2475. https://doi.org/10.1016/j.physb.2012.03.048

    Article  Google Scholar 

  11. Provatas N, Greenwood M, Athreya B, Goldenfeld N, Dantzig J (2005) Multiscale modeling of solidification: phase-field methods to adaptive mesh refinement. Int J Mod Phys B 19:4525–4565. https://doi.org/10.1142/S0217979205032917

    Article  Google Scholar 

  12. Feng W, Xu QY, Liu BC (2002) Microstructure simulation of aluminum alloy using parallel computing technique. ISIJ Int 42:702–707. https://doi.org/10.2355/isijinternational.42.702

    Article  Google Scholar 

  13. Jelinek B, Eshraghi M, Felicelli S, Peters JF (2014) Large-scale parallel lattice Boltzmann-cellular automaton model of two-dimensional dendritic growth. Comput Phys Commun 185:939–947. https://doi.org/10.1016/j.cpc.2013.09.013

    Article  Google Scholar 

  14. Bauer M, Hotzer J, Jainta M (2015) Massively Parallel Phase-Field Simulations for Ternary Eutectic Directional Solidification. https://doi.org/10.1145/2807591.2807662

  15. George WL, Warren JA (2002) A parallel 3D dendritic growth simulator using the phase-field method. J Comput Phys 177:264–283. https://doi.org/10.1006/jcph.2002.7005

    Article  MATH  Google Scholar 

  16. Knezevic M, Savage DJ (2014) A high-performance computational framework for fast crystal plasticity simulations. Comp Mater Sci 83:101–106. https://doi.org/10.1016/j.commatsci.2013.11.012

    Article  Google Scholar 

  17. Shibuta Y, Oguchi K, Suzuki T (2012) Large-scale molecular dynamics study on evolution of grain boundary groove of iron. ISIJ Int 52:2205–2209. https://doi.org/10.2355/isijinternational.52.2205

    Article  Google Scholar 

  18. Guo YQ, Luo S, Wang WL, Zhu MY (2022) A GPU-accelerated 3D PF-LBM modelling of multi-dendritic growth in an undercooled melt of Fe-C binary alloy. J Mater Res Technol 17:2059–2072. https://doi.org/10.1016/j.jmrt.2022.01.132

    Article  Google Scholar 

  19. Aoki T, Ogawa S, Yamanaka A (2011) Multiple-GPU scalability of phase-field simulation for dendritic solidification. Progress Nucl Sci Technol 2:639–642

    Article  Google Scholar 

  20. Ma CY, Jia JF, Liu Z, Zhang K, Huang JQ, Wang XY (2022) Simulation of three-dimensional phase field model with LBM method using OpenCL. J Supercomput. https://doi.org/10.1007/s11227-022-04321-w

    Article  Google Scholar 

  21. Zaeem MA (2015) Advances in modeling of solidification microstructures. Jom-Us 67:1774–1775. https://doi.org/10.1007/s11837-015-1488-3

    Article  Google Scholar 

  22. Yamazaki M, Natsume Y, Harada H, Ohsasa K (2006) Numerical simulation of solidification structure formation during continuous casting in Fe-0.7mass%C alloy using cellular automaton method. ISIJ Int 46:903–908. https://doi.org/10.2355/isijinternational.46.903

    Article  Google Scholar 

  23. Isobe K (2010) Effect of Mg addition on solidification structure of low carbon steel. ISIJ Int 50:1972–1980. https://doi.org/10.2355/isijinternational.50.1972

    Article  Google Scholar 

  24. Luo S, Zhu MY, Louhenkilpi S (2012) Numerical simulation of solidification structure of high carbon steel in continuous casting using cellular automaton method. ISIJ Int 52:823–830. https://doi.org/10.2355/isijinternational.52.823

    Article  Google Scholar 

  25. Bandini S, Mauri G, Serra R (2001) Cellular automata: from a theoretical parallel computational model to its application to complex system. Parallel Comput 27:539–553. https://doi.org/10.1016/S0167-8191(00)00076-4

    Article  MathSciNet  MATH  Google Scholar 

  26. Ferrando N, Gosálvez MA, Cerdá J, Gadea R, Sato K (2011) Octree-based, GPU implementation of a continuous cellular automaton for the simulation of complex, evolving surfaces. Comput Phys Commun 182:628–640. https://doi.org/10.1016/j.cpc.2010.11.004

    Article  MATH  Google Scholar 

  27. Blecic I, Cecchini A, Trunfio GA (2013) Cellular automata simulation of urban dynamics through GPGPU. J Supercomput 65:614–629. https://doi.org/10.1007/s11227-013-0913-z

    Article  Google Scholar 

  28. Campos RS, Lobosco M, dos Santos RW (2014) A GPU-based heart simulator with mass-spring systems and cellular automaton. J Supercomput 69:1–8. https://doi.org/10.1007/s11227-014-1199-5

    Article  Google Scholar 

  29. Wang JJ, Meng HJ, Yang J, Xie Z (2021) A fast method based on GPU for solidification structure simulation of continuous casting billets. J Comput Sci-Neth. https://doi.org/10.1016/j.jocs.2020.101265

    Article  Google Scholar 

  30. Yang J, Xie Z, Ji ZP, Meng HJ (2014) Real-time heat transfer model based on variable non-uniform grid for dynamic control of continuous casting billets. ISIJ Int 54:328–335. https://doi.org/10.2355/isijinternational.54.328

    Article  Google Scholar 

  31. Xie Z, Yang J (2015) Calculation of solidification-related thermophysical properties of steels based on Fe-C Pseudobinary phase diagram. Steel Res Int 86:766–774. https://doi.org/10.1002/srin.201400191

    Article  Google Scholar 

  32. Thévoz PH, Desbiolles JL, Rappaz M (1989) Modeling of equiaxed microstructure formation in casting. Metall Mater Trans A 20:311–322. https://doi.org/10.1007/BF02670257

    Article  Google Scholar 

  33. Akagiri T, Natsume Y, Ohsasa K, Matsuura K (2008) Evaluation of crystal multiplication at mold wall during solidification of casting. ISIJ Int 48:355–361. https://doi.org/10.2355/isijinternational.48.355

    Article  Google Scholar 

  34. Biscuola VB, Martorano MA (2008) Mechanical blocking mechanism for the columnar to equiaxed transition. Metall Mater Trans A 39a:2885–2895. https://doi.org/10.1007/s11661-008-9643-x

    Article  Google Scholar 

  35. Cheng J, Grossman M, McKercher T (2014) Professional CUDA C Programming. Wrox, Birmingham

    Google Scholar 

  36. Mattson TG, He Y, Koniges AE (2019) The OpenMP common core: making OpenMP simple gain

  37. Pacheco P (2011) An introduction to parallel programming. Morgan Kaufmann, San Francisco

    Google Scholar 

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Acknowledgements

Funds: This work was supported by the National Natural Science Foundation of China (No.51634002 and No.61703084); and the Fundamental Research Funds for the Central Universities (No. N224001-8).

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  1. School of Information Science and Engineering, Northeastern University, Shenyang, 110819, China

    Jingjing Wang, Hongji Meng, Jian Yang & Zhi Xie

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Wang, J., Meng, H., Yang, J. et al. Multi-GPU accelerated cellular automaton model for simulating the solidification structure of continuous casting bloom. J Supercomput 79, 4870–4894 (2023). https://doi.org/10.1007/s11227-022-04839-z

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