Neural Network with Local Converging Input for Unstructured-Grid Computational Fluid Dynamics

Abstract

In recent years, surrogate models based on deep neural networks have been widely used to solve partial differential equations for fluid flow physics. This kind of model focuses on global interpolation of the training data and thus requires a large network structure. The process is both time consuming and computationally costly. In the present study, we develop a neural network with local converging input (NNLCI) for high-fidelity prediction using unstructured data. The framework uses the local domain of dependence with converging coarse solutions as input, thereby greatly reducing computational resource and training time. As a validation case, the NNLCI method is applied to study two-dimensional inviscid supersonic flows in channels with bumps. Different bump geometries and locations are examined to benchmark the effectiveness and versatility of this new approach. The NNLCI method can accurately and efficiently capture the structure and dynamics of the entire flowfield, including regions with shock discontinuities. For a new bump configuration, the method can perform prediction with only one neural network, eliminating the need for repeated training of multiple networks for different geometries. A saving of computing wall time is achieved by several orders of magnitude against the high-fidelity simulation with the same level of accuracy. The demand on training data is modest, and the training data can be allocated sparsely. These features are especially advantageous compared with conventional global-to-global deep learning methods and physics-informed methods.