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Simulation of three-dimensional phase field model with LBM method using OpenCL

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Abstract

Multi-field coupled three-dimensional phase field model is a research hotspot for simulating the growth mechanism of solidification microstructure. Single-CPU has become the main bottleneck in the development of phase field model due to its computing power and storage limitations. Based on this, the PF-LBM model of three-dimensional dendritic growth of supercooled pure substance solution under flow is established in this study. We take the succinonitrile (SCN) as the research object and use OpenCL heterogeneous parallel technology to realize the parallel solution. Firstly, the performance of the phase field model solution process is analyzed to find out the time-consuming modules; then, a parallel solution is proposed, and the preliminary parallelization of the phase field model is realized; finally, the problems existing in the parallel algorithm are optimized. The experimental results show that compared with the serial algorithm on the CPU platform under the same conditions, the speedup ratio reaches the highest when the computing scale is 128*128*128, which is 62.10. And the average speedup is 57.46. The scale after parallel is also expanded from 189*189*189 to 357*357*357, which effectively solves the problems existing in single-CPU simulation.

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References

  1. Langer JS, Müller-Krumbhaar H (1978) Theory of dendritic growth-i. Elements of a stability analysis. Acta Metall 26(11):1681–1687

    Article  Google Scholar 

  2. Steinbach I (2009) Phase-field models in materials science. Model Simul Mater Sci Eng 17(7):073001

    Article  Google Scholar 

  3. Xu H, Pei Y, Li F, Fang D (2018) A multi-scale and multi-field coupling nonlinear constitutive theory for the layered magnetoelectric composites. J Mech Phys Solids 114:143–157

    Article  MathSciNet  Google Scholar 

  4. Kim SG, Kim WT, Suzuki T (1998) Interfacial composition of solid and liquid in a phase-field model with finite interface thickness for isothermal solidification in binary alloys. Phys Rev E 58(3):3316

    Article  Google Scholar 

  5. Langer JS (1986) Directions in condensed matter physics. In: Models of Pattern Formation in First-order Phase Transition, pp 165–186

  6. Karma A, Rappel W-J (1996) Numerical simulation of three-dimensional dendritic growth. Phys Rev Lett 77(19):4050

    Article  Google Scholar 

  7. Sun Y, Beckermann C (2009) Effect of solid-liquid density change on dendrite tip velocity and shape selection. J Cryst Growth 311(19):4447–4453

    Article  Google Scholar 

  8. Frisch U, Dhumieres D, Hasslacher B et al (1987) Lattice Gas Hydrodynamics in Two and Three Dimensions. Complex Syst 1(4):649–708

    MathSciNet  MATH  Google Scholar 

  9. Chen S, Doolen GD (1998) Lattice Boltzmann method for fluid flows. Annu Rev Fluid Mech 30(1):329–364

    Article  MathSciNet  Google Scholar 

  10. He X, Luo L-S (1997) Theory of the lattice Boltzmann method: from the Boltzmann equation to the lattice Boltzmann equation. Phys Rev E 56(6):6811

    Article  Google Scholar 

  11. Aidun CK, Clausen JR (2010) Lattice-Boltzmann method for complex flows. Annu Rev Fluid Mech 42:439–472

    Article  MathSciNet  Google Scholar 

  12. Zhang A, Guo Z-P, Xiong S-M (2017) Phase-field-lattice Boltzmann study for lamellar eutectic growth in a natural convection melt. China Foundry 14(5):373–378

    Article  Google Scholar 

  13. Zhi-pin W (2014) Phase-field simulation of alloy dendritic growth based on LBM algorithm in force flow. J Lanzhou Univ Technol 40(2):18–22

    Google Scholar 

  14. Rojas R, Takaki T, Ohno M (2015) A phase-field-lattice Boltzmann method for modeling motion and growth of a dendrite for binary alloy solidification in the presence of melt convection. J Comput Phys 298:29–40

    Article  MathSciNet  Google Scholar 

  15. Luo S, Wang P, Wang W et al (2020) PF-LBM modelling of dendritic growth and motion in an undercooled melt of Fe-C binary alloy. Metall Mater Trans B 51(5):2268–2284

    Article  Google Scholar 

  16. Pan S, Zhu M, Rettenmayr M (2017) A phase-field study on the peritectic phase transition in Fe-C alloys. Acta Mater 132:565–575

    Article  Google Scholar 

  17. Hosseini SA, Darabiha N, Thévenin D (2020) Compressibility in lattice Boltzmann on standard stencils: effects of deviation from reference temperature. Philos Trans R Soc A 378(2175):20190399

    Article  MathSciNet  Google Scholar 

  18. Zhang T, Javadpour F, Yin Y, Li X (2020) Upscaling water flow in composite nanoporous shale matrix using lattice Boltzmann method. Water Resourc Res 56(4):e2019WR026007

    Article  Google Scholar 

  19. Alamsyah MNA, Simanjuntak CA, Bagustara BARH, Pradana WA, Gunawan PH (2017) Openmp analysis for lid driven cavity simulation using lattice Boltzmann method. In: 2017 5th International Conference on Information and Communication Technology (ICoIC7). IEEE, pp 1–6

  20. Basha M, Sidik NAC (2018) Numerical predictions of laminar and turbulent forced convection: lattice Boltzmann simulations using parallel libraries. Int J Heat Mass Transf 116:715–724

    Article  Google Scholar 

  21. Karma A, Rappel W-J (1998) Quantitative phase-field modeling of dendritic growth in two and three dimensions. Phys Rev E 57(4):4323

    Article  Google Scholar 

  22. Tong X, Beckermann C, Karma A (2001) Velocity and shape selection of dendritic crystals in a forced flow. In: Interactive Dynamics of Convection and Solidification, pp 47–56

  23. Li YB, Lee HG, Kim J (2011) A fast, robust, and accurate operator splitting method for phase-field simulations of crystal growth. J Cryst Growth 321(1):176–182

    Article  Google Scholar 

  24. Guo Z, Xiong SM (2015) On solving the 3-D phase field equations by employing a parallel-adaptive mesh refinement (Para-AMR) algorithm. Comput Phys Commun 190:89–97

    Article  MathSciNet  Google Scholar 

  25. Bing Z, Yuhong Z, Hong W, Weipeng C, Hua H (2019) Three-dimensional phase field simulation of dendritic morphology of Al-Si alloy. Rare Met Mater Eng 48(9):2835–2840

    Google Scholar 

  26. Takaki T (2014) Phase-field modeling and simulations of dendrite growth. ISIJ Int 54(2):437–444

    Article  Google Scholar 

  27. Lan CW, Liu CC, Hsu CM (2002) An adaptive finite volume method for incompressible heat flow problems in solidification. J Comput Phys 178(2):464–497

    Article  Google Scholar 

  28. Rosam J, Jimack PK, Mullis A (2007) A fully implicit, fully adaptive time and space discretisation method for phase-field simulation of binary alloy solidification. J Comput Phys 225(2):1271–1287

    Article  MathSciNet  Google Scholar 

  29. Du P, Weber R, Luszczek P, Tomov S, Peterson G, Dongarra J (2012) From CUDA to OpenCL: towards a performance-portable solution for multi-platform GPU programming. Parallel Comput 38(8):391–407

    Article  Google Scholar 

  30. You L, Yang E, Wang G (2020) A novel parallel image encryption algorithm based on hybrid chaotic maps with OpenCL implementation. Soft Comput 24(16):12413–12427

    Article  Google Scholar 

  31. Young-Schultz T, Lilge L, Brown S, Betz V (2020) Using OpenCL to enable software-like development of an FPGA-accelerated biophotonic cancer treatment simulator. In: Proceedings of the 2020 ACM/SIGDA International Symposium on Field-Programmable Gate Arrays, pp 86–96

  32. Kim J, Kim H, Lee JH, Lee J (2011) Achieving a single compute device image in OpenCL for multiple GPUs. ACM Sigplan Notices 46(8):277–288

    Article  Google Scholar 

  33. Habich J, Feichtinger C, Köstler H, Hager G, Wellein G (2013) Performance engineering for the lattice Boltzmann method on GPGPUs: architectural requirements and performance results. Comput Fluids 80:276–282

    Article  Google Scholar 

  34. Schreiber M, Neumann P, Zimmer S, Bungartz H-J (2011) Free-surface lattice-Boltzmann simulation on many-core architectures. Procedia Comput Sci 4:984–993

    Article  Google Scholar 

  35. Zhu C, Guo X, Feng L, Uwa Idemudia C, Jin X (2020) Simulation of three-dimensional eutectic growth multi-phase field based on OpenCL parallel. AIP Adv 10(2):025026

    Article  Google Scholar 

  36. Nan-Zhong H et al (2004) A unified incompressible lattice BGK model and its application to three-dimensional lid-driven cavity flow. Chin Phys 13(1):40

    Article  Google Scholar 

  37. Krishnamoorthy S, Baskaran M, Bondhugula U, Ramanujam J, Rountev A, Sadayappan P (2007) Effective automatic parallelization of stencil computations. ACM Sigplan Not 42(6):235–244

    Article  Google Scholar 

Download references

Acknowledgements

Fund projects: the Chunhui project of the Ministry of Education (No. QDCH2018001), Science and Technology Plan Project of Qinghai Province-Applied Basic Research Plan (No. 2019-ZJ-7034), and National Natural Science Foundation of China (No. 61762074, No. 62062059).

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Authors and Affiliations

  1. Department of Computer Technology and Applications, Qinghai University, Xining, 810016, Qinghai, China

    Chenyu Ma, Jinfang Jia, Kun Zhang, Jianqiang Huang & Xiaoying Wang

  2. Graduate School of Engineering, Nagasaki Institute of Applied Science, 536 Aba-machi, Nagasaki, 851-0193, Japan

    Zhen Liu

  3. Department of Computer Science and Technology, Tsinghua University, Beijing, 100084, China

    Jianqiang Huang

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  1. Chenyu Ma
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  2. Jinfang Jia
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Correspondence to Jinfang Jia.

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Ma, C., Jia, J., Liu, Z. et al. Simulation of three-dimensional phase field model with LBM method using OpenCL. J Supercomput 78, 11092–11110 (2022). https://doi.org/10.1007/s11227-022-04321-w

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