An Improved Lattice Boltzmann Method Fluid Prediction Model Based on A Two-Layer Neural Controlled Differential Equation

Compared to traditional computational fluid dynamics methods, the Lattice Boltzmann Method (LBM) has the advantages of a simple program structure, adaptability to complex boundaries and ease of parallel computation. However, as LBM is an explicit algorithm, there are multiple iterations during the computation, which leads to an increase in numerical dissipation. In this paper, the LBM is improved on the basis of the Neural Control Differential Equation (NCDE). A neural control lattice Boltzmann differential equation (LBM-NCDE) approach is proposed. The lattice Boltzmann method is first used to extract the temporal and spatial features of the fluid and discretise them. Secondly, a two-layer NCDE is designed, one for the temporal processing and one for the spatial processing. In particular, the NDE for spatial processing can be considered as an interpretation based on a convolutional neural network. They are then combined into a computational framework for predicting the lattice Boltzmann equation of state for the fluid at the next moment. Finally the accuracy of the computational framework was verified using laminar flow experiments. The experiments show that the method is very effective compared to traditional LBM methods, with a significant improvement in the accuracy of the prediction of fluid velocity and pressure.