Physics-constrained and flow-field-message-informed graph neural network for solving unsteady compressible flows

Abstract

With the increasing use of deep neural networks as surrogate models for accelerating computational simulations in mechanics, the application of artificial intelligence in computational fluid dynamics has seen renewed interest in recent years. However, the application of deep neural networks for flow simulations has mainly concentrated on relatively simple cases of incompressible flows. The strongly discontinuous structures that appear in compressible flows dominated by convection, such as shock waves, introduce significant challenges when approximating the nonlinear solutions or governing equations. In this work, we propose a novel physics-constrained, flow-field-message-informed (FFMI) graph neural network for spatiotemporal flow simulations of compressible flows involving strong discontinuities. To enhance the nonlinear approximation capability of strong discontinuities, a shock detector method is leveraged to extract the local flow-field messages. These messages are embedded into the graph representation to resolve the discontinuous solutions accurately. A new FFMI sample-and-aggregate-based message-passing layer, which aggregates the edge-weighted attributes with node features on different hop layers, is then developed to diffuse and process the flow-field messages. Furthermore, an end-to-end paradigm is established within the encoder–decoder framework to transform the extracted information from the flow field into latent knowledge about the underlying fluid mechanics. Finally, a variety of one- and two-dimensional cases involving strong shock waves are considered to demonstrate the effectiveness and generalizability of the proposed FFMI graph neural network.