Super-resolution of turbulent reacting flows on complex meshes using graph neural networks

TL;DR

This study uses the inherent flexibility of GNNs featuring message passing layers to develop a methodology for reconstructing unresolved small-scale structures from low-resolution data on complex meshes to enhance the accuracy of coarse-grained simulations on complex meshes.

Abstract

State-of-the-art deep learning models have been extensively utilized to reconstruct small-scale structures from coarse-grained data in turbulent flows. However, their application has predominantly been restricted to structured uniform meshes, limiting their applicability to data associated with complex geometries that are typically simulated on structured non-uniform or unstructured meshes. Machine learning (ML) models based on graph neural networks (GNNs), known for their ability to process unstructured data, offer a promising alternative. In this study, we leverage the inherent flexibility of GNNs featuring message passing layers to develop a methodology for reconstructing unresolved small-scale structures from low-resolution data on complex meshes. The accuracy of the proposed approach is demonstrated using two cases: a reacting channel flow on a structured non-uniform mesh, and a reacting hydrogen fueled internal combustion (IC) engine featuring an unstructured mesh. Evaluation of results based on visual agreement, statistical metrics, and cumulative error reduction indicates the effectiveness of the method in accurately reconstructing fine-scale features. Overall, this study provides a pathway for integrating data-driven small-scale reconstruction and subgrid-scale modeling to enhance the accuracy of coarse-grained simulations on complex meshes.

Figures (10)

• Figure 1: A schematic of the GNN framework for super-resolution (left), and message passing layer (right) showing edge feature update, edge feature aggregation, and node feature update.
• Figure 2: Volumetric rendering of temperature inside the channel, with the flame surface represented in black color.
• Figure 3: Flame front isosurface superimposed on the normalized velocity magnitude distribution on the engine midplane.
• Figure 4: Error reduction by GNN compared to trilinear interpolation and CNN baseline for Case 1. Column 1: Contours of key variables shown for the center-plane along $z$. Columns 2, 3, and 4: Contours of absolute errors $\epsilon$ between ground truth (DNS solution) and the results of interpolation, CNN, and GNN.
• Figure 5: Cumulative error percentage for selected scalars across all upsampling methods in Case 1.