Patch-Based Modelling of Turbulent Flows using Graph Neural Networks
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High-fidelity CFD simulations are expensive, time-consuming and require substantial effort during setup. Turbulent flows in particular require fine spatial and temporal resolution to accurately capture all the relevant physical scales, which further increases computational burden. These challenges have motivated a growing interest in ML-based approaches that can predict entire flow fields directly from geometric and input parameters. Once trained, such ML models enable fast predictions and at a significantly lower computational cost than traditional solvers. Despite their merits, training of such models is limited by the availability of fully-resolved simulation data required for robust generalization. Domain decomposition techniques, as demonstrated by Ranade et al. [1], have been successful in reducing training requirements. In their work, CNN-based autoencoders are used to compress PDE solutions and governing conditions into low-dimensional latent vectors. A flux conservation network then couples neighboring subdomains to solve for the global field. However, the use of Signed Distance Fields (SDFs) on Cartesian grids struggles to accurately capture flow near curved boundaries. To address these concerns, we employ GNNs in conjunction with unstructured meshes. We represent the computational domain using a block-structured grid that is morphed alongside geometrical variations in the input data [2]. In combination with GNNs, this technique can capture varied flow configurations and the decomposition into patches generates numerous training samples. We compare this approach to other common geometry representations. Additionally, we replace the solution latent vectors from [1] with low-dimensional representations based on spectral coordinates [3], further reducing training costs. The different methods are evaluated on a challenging test case of turbulent flow around two cylinders with varying cylinder positions. The study thus shows that our methodology can effectively reduce training samples and computational costs while achieving improved accuracy for flow prediction in complex geometries.
