TSI-SD: A time-sequence-involved space discretization neural network for passive scalar advection in a two-dimensional unsteady flow

Abstract

Numerical simulation of fluid is a great challenge as it contains extremely complicated variations with a high Reynolds number. Usually, very high-resolution grids are required to capture the very fine changes during the physical process of the fluid to achieve accurate simulation, which will result in a vast number of computations. This issue will continue to be a bottleneck problem until a deep-learning solution is proposed to utilize large-scale grids with adaptively adjusted coefficients during the spatial discretization procedure—instead of traditional methods that adopt small grids with fixed coefficients—so that the computation cost is dramatically reduced and accuracy is preserved. This breakthrough will represent a significant improvement in the numerical simulation of fluid. However, previously proposed deep-learning-based methods always predict the coefficients considering only the spatial correlation among grids, which provides relatively limited context and thus cannot sufficiently describe patterns along the temporal dimension, implying that the spatiotemporal correlation of coefficients is not well learned. We propose the time-sequence-involved space discretization neural network (TSI-SD) to extract grid correlations from spatial and temporal views together to address this problem. This novel deep neural network is transformed from a classic CONV-LSTM backbone with careful modification by adding temporal information into two-dimensional spatial grids along the x-axis and y-axis separately at the first step and then fusing them through a post-fusion neural network. After that, we combine the TSI-SD with the finite volume format as an advection solver for passive scalar advection in a two-dimensional unsteady flow. Compared with previous methods that only consider spatial context, our method can achieve higher simulation accuracy, while computation is also decreased as we find that after adding temporal data, one of the input features, the concentration field, is redundant and should no longer be adopted during the spatial discretization procedure, which results in a sharp decrease of parameter scale and achieves high efficiency. Comprehensive experiments, including a comparison with SOTA methods and sufficient ablation studies, were carried out to verify the accurate and efficient performance and highlight the advantages of the proposed method.