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Anisotropic mesh spacing prediction using neural networks

Callum Lock, Oubay Hassan, Ruben Sevilla, Jason Jones

TL;DR

The paper addresses the challenge of generating near-optimal anisotropic meshes for unseen CFD scenarios by leveraging historical high-fidelity data. It proposes a pipeline that computes a target metric from high-quality simulations, transfers it to a common background mesh via mesh morphing and conservative metric intersection, and trains an ANN to predict the metric tensor (directions and spacings) on the background mesh for new conditions. The authors introduce a two-ANN architecture (one for spacings and one for anisotropy directions) and an encoding strategy that enforces metric properties, validated on an ONERA M6 wing and a geometrically parametrised full aircraft, showing accurate spacing fields and preserved aerodynamic quantities. This approach enables high-quality initial meshes for design and analysis workflows with potentially reduced reliance on iterative mesh adaptation, facilitating faster CFD studies and design cycles.

Abstract

This work presents a framework to predict near-optimal anisotropic spacing functions suitable to perform simulations with unseen operating conditions or geometric configurations. The strategy consists of utilising the vast amount of high fidelity data available in industry to compute a target anisotropic spacing and train an artificial neural network to predict the spacing for unseen scenarios. The trained neural network outputs the metric tensor at the nodes of a coarse background mesh that is then used to generate meshes for unseen cases. Examples are used to demonstrate the effect of the network hyperparameters and the training dataset on the accuracy of the predictions. The potential is demonstrated for examples involving up to 11 geometric parameters on CFD simulations involving a full aircraft configuration.

Anisotropic mesh spacing prediction using neural networks

TL;DR

The paper addresses the challenge of generating near-optimal anisotropic meshes for unseen CFD scenarios by leveraging historical high-fidelity data. It proposes a pipeline that computes a target metric from high-quality simulations, transfers it to a common background mesh via mesh morphing and conservative metric intersection, and trains an ANN to predict the metric tensor (directions and spacings) on the background mesh for new conditions. The authors introduce a two-ANN architecture (one for spacings and one for anisotropy directions) and an encoding strategy that enforces metric properties, validated on an ONERA M6 wing and a geometrically parametrised full aircraft, showing accurate spacing fields and preserved aerodynamic quantities. This approach enables high-quality initial meshes for design and analysis workflows with potentially reduced reliance on iterative mesh adaptation, facilitating faster CFD studies and design cycles.

Abstract

This work presents a framework to predict near-optimal anisotropic spacing functions suitable to perform simulations with unseen operating conditions or geometric configurations. The strategy consists of utilising the vast amount of high fidelity data available in industry to compute a target anisotropic spacing and train an artificial neural network to predict the spacing for unseen scenarios. The trained neural network outputs the metric tensor at the nodes of a coarse background mesh that is then used to generate meshes for unseen cases. Examples are used to demonstrate the effect of the network hyperparameters and the training dataset on the accuracy of the predictions. The potential is demonstrated for examples involving up to 11 geometric parameters on CFD simulations involving a full aircraft configuration.

Paper Structure

This paper contains 13 sections, 13 equations, 16 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Anisotropic mesh spacing and control using a background mesh
  4. Feed-forward neural networks
  5. Mesh morphing for geometrically parametrised domains
  6. Near-optimal anisotropic mesh spacing prediction
  7. Computation of the target anisotropic spacing in the computational mesh
  8. Transfer of the target anisotropic spacing to a background mesh
  9. ANN architecture to predict anisotropic spacing
  10. Numerical examples
  11. Anisotropic spacing predictions on the ONERA M6 wing at various inflow conditions
  12. Anisotropic spacing predictions on a geometrically parametrised aircraft
  13. Concluding remarks

Figures (16)

  • Figure 1: Representation of a tetrahedral element with anisotropic spacing given by three mutually orthogonal directions, $\mathbf{e}_1$, $\mathbf{e}_2$ and $\mathbf{e}_3$, and the desired spacing in each direction, $\delta_1$, $\delta_2$ and $\delta_3$.
  • Figure 2: Schematic representation of the metric interpolation for a point inside a tetrahedral element.
  • Figure 3: Schematic representation of a feed-forward ANN.
  • Figure 4: ONERA M6 wing: Pressure coefficient, $C_p$, for three different flow conditions.
  • Figure 5: ONERA M6 wing: MAE for the spacings ($\delta_i$) and angles ($\alpha_i$) as a function of the number of layers and number of neurons in each layer employing the first model of Table \ref{['tb:NNTypes']}.
  • ...and 11 more figures

Theorems & Definitions (3)

  • Remark 1
  • Remark 2
  • Remark 3