A GNN-based Surrogate Model Involving Flow-field Message for Spatio-temporal Flow Simulations of Compressible Flows
Traditional numerical methods are grid-based numerical discretization or integration approaches,which introduce low computational efficiency,high time consumption,and require expensive computing resources.This paper propose a GNN-based surrogate model involving flow-field message for solving unsteady compressible flows with strong discontinuities.As first step,the inherent consistence between CFD approaches and GNN methods is analyzed in depth,which mathematically clarifies clarifies the operator objects and tasks during the model training and guides the designing of the model architecture.Moreover,to enhance nonlinear approximation capability of strong discontinuities,a shock detector method is leveraged to extract the local flow field messages,which are embedded into the graph representations to resolve the discontinuous solutions well.Then,a new flow-field-message-informed and SAGE(Sample and Aaggregate)-based message passing layer(FFMI-SAGE),aggregating the edge-weighted attributes with node features on different hop layers,is developed to diffuse and process the flow field messages.Furthermore,an end-to-end paradigm is conducted within the Encoder-Decoder framework to transform the extracted information from flow field into the latent knowledge about the underlying fluid mechanics.Finally,a variety of test cases including the sod tube problem,Shu-Osher problem and two-dimensional Riemann problem are employed to demonstrate the effectiveness and generalizability of the proposed FFMI-GNN model.The results show that in both one-and two-dimensional problems,the model training can converge quickly,and the relative error of variables is on the order of O(10-6)～O(10-7).For predicting flow fields outside the training set,this model has attractive generalizability and greatly improves the efficiency of flow field calculation.
NETL
NSTL
万方数据
维普
