Research on Lattice Boltzmann Solution of Generalized Convection Diffusion Equation Based on Physical Fusion Neural Network

Wang Yahui; Xiao Hao; Ma Yu; Xie Yuchen; Chi Honghang

doi:10.13832/j.jnpe.2024.070062

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Wang Yahui, Xiao Hao, Ma Yu, Xie Yuchen, Chi Honghang. Research on Lattice Boltzmann Solution of Generalized Convection Diffusion Equation Based on Physical Fusion Neural Network[J]. Nuclear Power Engineering. doi: 10.13832/j.jnpe.2024.070062

Citation:

Wang Yahui, Xiao Hao, Ma Yu, Xie Yuchen, Chi Honghang. Research on Lattice Boltzmann Solution of Generalized Convection Diffusion Equation Based on Physical Fusion Neural Network[J]. Nuclear Power Engineering. doi: 10.13832/j.jnpe.2024.070062

Citation:

Wang Yahui, Xiao Hao, Ma Yu, Xie Yuchen, Chi Honghang. Research on Lattice Boltzmann Solution of Generalized Convection Diffusion Equation Based on Physical Fusion Neural Network[J]. Nuclear Power Engineering. doi: 10.13832/j.jnpe.2024.070062

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Research on Lattice Boltzmann Solution of Generalized Convection Diffusion Equation Based on Physical Fusion Neural Network

doi: 10.13832/j.jnpe.2024.070062

Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-Sen University, Zhuhai, Guangdong, 519082, China

Received Date: 2024-07-31
Rev Recd Date: 2024-08-21

Available Online: 2025-01-15

Abstract

Abstract

This paper proposes the physics fusion neural network based lattice Boltzmann method (PFNN-LBM) for solving the nonlinear convection-diffusion equations. The unified discrete-velocity Boltzmann equation for equations with different characteristics is established under lattice Boltzmann method, and solved using the parameterize physics–informed neural network with a single network. The PFNN-LBM can simultaneously solve governing equations with different forms and different physical parameters within one single training. Four types of equations are considered to verify the accuracy and adaptability of proposed PFNN-LBM, including diffusion equation, nonlinear heat conduct equation, Sine–Gordon equation, and Burgers–Fisher equation, with different physical parameters. The two-group neutron diffusion equations are also tested. The calculation results show that the proposed PFNN-LBM can solve equations for different forms and physical parameters with high accuracy, and only one training is required. This work can provide a novel framework for solving different types of equations efficiently and flexibly, and for engineering application, this work may have outstanding advantages in multi-physics coupling calculations.
- Physics–informed neural network,
- Lattice Boltzmann,
- Deep learning,
- Nonlinear convection–diffusion equations

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References(12)

References

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