An accelerated lattice Boltzmann method for natural convection coupled with convolutional neural network

Abstract

A novel approach is proposed in the present study, which combines the lattice Boltzmann method (LBM) with convolutional neural networks and is suitable for square cavity natural convection and conjugate natural convection problems, exhibiting remarkable acceleration capabilities and potentials. The density distribution function obtained from LBM at time t and the temperature distribution function at time t+Δt under different Rayleigh numbers (Ra) are, respectively, utilized as input and output datasets for training and comparison in three convolutional neural networks, aiming to select the optimal coupling model, namely, half-Res-Unet. The coupling model can accurately simulate the natural convection in a square cavity within six times the upper limit of the Ra under the training condition, which can save the central processing unit (CPU) calculation time and the iteration steps by up to 29.2% and 30.3%, respectively. The coupling model is further extended in the current study to incorporate conjugate natural convection, enabling the accurate simulation of temperature distribution under training conditions with a thermal conductivity ratio (Ka) of 25 and an upper limit of Ra increased by 20 times. The corresponding maximum relative errors for the average Nusselt numbers (Nu) are found to be 1.8% and 0.7%, respectively, providing strong evidence for the generalization capability of the coupling model. Furthermore, the coupling model demonstrates a remarkable acceleration performance, as evidenced by its ability to reduce the CPU calculation time by up to 39.6% and iteration steps in the simulation process by 36.5%. It offers valuable insights into the integration of LBM with machine learning techniques, thereby enhancing the computational efficiency of LBM.