Neural Network with Local Converging Input (NNLCI) for Supersonic Flow Problems with Unstructured Grids
This addresses the problem of high computational costs for researchers and engineers in computational fluid dynamics, though it appears incremental as it builds on existing surrogate model approaches.
The study tackled the computational inefficiency of deep neural network surrogate models for solving partial differential equations in supersonic flow problems by developing a neural network with local converging input (NNLCI) that reduces resource usage and training time, as validated on inviscid supersonic flows in channels with bumps.
In recent years, surrogate models based on deep neural networks (DNN) have been widely used to solve partial differential equations, which were traditionally handled by means of numerical simulations. This kind of surrogate models, however, focuses on global interpolation of the training dataset, and thus requires a large network structure. The process is both time consuming and computationally costly, thereby restricting their use for high-fidelity prediction of complex physical problems. In the present study, we develop a neural network with local converging input (NNLCI) for high-fidelity prediction using unstructured data. The framework utilizes the local domain of dependence with converging coarse solutions as input, which greatly reduces computational resource and training time. As a validation case, the NNLCI method is applied to study inviscid supersonic flows in channels with bumps. Different bump geometries and locations are considered to benchmark the effectiveness and versability of the proposed approach. Detailed flow structures, including shock-wave interactions, are examined systematically.