A machine learning approach to predict near-optimal meshes for turbulent compressible flow simulations (2406.16057v1)

Abstract: This work presents a methodology to predict a near-optimal spacing function, which defines the element sizes, suitable to perform steady RANS turbulent viscous flow simulations. The strategy aims at utilising existing high fidelity simulations to compute a target spacing function and train an artificial neural network (ANN) to predict the spacing function for new simulations, either unseen operating conditions or unseen geometric configurations. Several challenges induced by the use of highly stretched elements are addressed. The final goal is to substantially reduce the time and human expertise that is nowadays required to produce suitable meshes for simulations. Numerical examples involving turbulent compressible flows in two dimensions are used to demonstrate the ability of the trained ANN to predict a suitable spacing function. The influence of the NN architecture and the size of the training dataset are discussed. Finally, the suitability of the predicted meshes to perform simulations is investigated.

• The paper demonstrates that a feed-forward ANN predicts near-optimal mesh spacing with an R² above 0.98 using limited training data.
• It computes target spacing from pressure and Mach number, transferring these metrics onto a coarser mesh for efficient ANN training.
• Extensive numerical validation shows that the method reduces human effort while effectively handling stretched elements and variable geometries.

Predicting Near-Optimal Meshes for Turbulent Compressible Flow Simulations Using Machine Learning

The paper "A machine learning approach to predict near-optimal meshes for turbulent compressible flow simulations" by Sanchez-Gamero et al. proposes an innovative methodology for generating near-optimal meshes for computational fluid dynamics (CFD) simulations involving turbulent, compressible flow. This task, typically labor-intensive and requiring significant expertise, is tackled through the use of artificial neural networks (ANNs) trained on high-fidelity simulation data. This method aims to reduce both the time and human effort needed to produce suitable meshes, thereby streamlining the CFD simulation workflow.

Methodology

The proposed approach comprises three major stages:

1. Target Spacing Function Computation: The mesh spacing required to capture all relevant flow features in a given simulation is computed. This involves evaluating the Hessian matrix of a chosen key variable—pressure and Mach number in this paper. These metrics are utilized due to their ability to highlight different critical regions in the flow solution.
2. Transfer of Spacing Function to Background Mesh: The computed spacing is interpolated onto a coarser, background mesh. This process provides a consistent and manageable number of output nodes for the ANN, facilitating smoother and more reliable training.
3. Training and Prediction with ANN: A feed-forward ANN is trained using historical simulation data. The trained network predicts the spacing function for new simulations under varying operating conditions or geometric configurations.

Key Contributions

The paper addresses several notable challenges intrinsic to mesh generation for turbulent flows:

1. Handling Stretched Elements: It provides a systematic approach to tackle issues related to highly stretched elements, especially in boundary layers. This includes a smoothing procedure for the pressure field, which prevents small normal variations from dominating the spacing calculations.
2. Multiple Key Variables: In addition to pressure, the Mach number is used as a key variable to ensure the features in the wake and other high-gradient regions are adequately captured.
3. Mesh Morphing for Variable Geometries: For problems involving variable geometries, the background mesh is morphed using linear elasticity principles. This ensures consistency in the number of mesh nodes despite changes in geometric configurations.
4. Extensive Numerical Validation: The efficacy of the approach is validated using numerical examples that include varying flow conditions and geometries. The influence of ANN architecture and training dataset size on prediction accuracy is also analyzed.

Strong Numerical Results

The results demonstrate the method's robustness and accuracy. For instance, using just 40 training cases, the ANN achieved a coefficient of determination (R²) greater than 0.98 in predicting the mesh spacing for variable operating conditions. The paper also shows that finer background meshes can lead to even more precise spacing predictions but at the cost of increased training time.

Practical and Theoretical Implications

By automating the generation of near-optimal meshes, this research holds significant practical implications for the CFD community. It reduces the dependence on human expertise, decreases the time required for mesh generation, and potentially lowers the associated carbon emissions due to reduced computational demand. Theoretically, this work demonstrates the viability and effectiveness of machine learning in complex engineering simulations, paving the way for its application in other domains requiring substantial human intervention.

Speculation on Future Developments

Future research could extend this approach in several ways. One promising direction is the incorporation of anisotropic metrics, which would enhance the mesh's capability to capture directional flow features with greater fidelity. Additionally, integrating reinforcement learning could enable the dynamic refinement of the mesh during the simulation itself, offering a real-time adaptive meshing solution.

Conclusion

The paper by Sanchez-Gamero et al. provides a comprehensive and practical solution for predicting near-optimal meshes for CFD simulations of turbulent, compressible flows. By leveraging machine learning, it offers a significant step forward in automating and optimizing the mesh generation process. This work underlines the transformative potential of AI in computational engineering and opens new avenues for research and application in CFD and beyond.