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A machine learning approach to predict near-optimal meshes for turbulent compressible flow simulations

Sergi Sanchez-Gamero, Oubay Hassan, Ruben Sevilla

TL;DR

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.

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.

A machine learning approach to predict near-optimal meshes for turbulent compressible flow simulations

TL;DR

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.

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.
Paper Structure (17 sections, 20 equations, 28 figures, 7 tables)

This paper contains 17 sections, 20 equations, 28 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Governing equations
  4. Non-uniform rational B-splines
  5. Spacing function using a background mesh
  6. Mesh morphing
  7. Feed-forward neural networks
  8. Near-optimal spacing function prediction using ANNs
  9. Computation of the target spacing in the computational mesh
  10. Computation of the Hessian matrix
  11. Choice of the key variables
  12. Computation of the target spacing in the inflation layer
  13. Computation of the target spacing in the background mesh
  14. Numerical results
  15. Prediction of the spacing for variable operating conditions
  16. ...and 2 more sections

Figures (28)

  • Figure 1: Sketch of a multi-layer feed-forward ANN.
  • Figure 2: Solution obtained on a fine mesh for $Re_\infty = 6.5 \times 10^{6}$, $M_{\infty} = 0.811$, and $\alpha= 0.27^\circ$.
  • Figure 3: Meshes obtained by varying the minimum spacing using the pressure as key variable for the solution of Figure \ref{['fig:solution']}(a).
  • Figure 4: Meshes obtained with the minimum spacing provided by pressure as key variable and with three different approaches to evaluate the Hessian for the solution of Figure \ref{['fig:solution']}(a).
  • Figure 5: Detail of the three meshes of Figure \ref{['fig:meshPHessian']} near the region where the shock of the upper surface interacts with the boundary layer.
  • ...and 23 more figures

Theorems & Definitions (4)

  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4