Towards Incompressible Laminar Flow Estimation Based on Interpolated Feature Generation and Deep Learning
Abstract
:1. Introduction
- Firstly, we create the raw laminar flow datasets around different obstacles using the CFD solver FEATool [19]. Then, we generate novel learning input and output interpolated CFD features using the mesh-grid and grid-data computations on these raw simulated datasets.
- Second, we build a deep U-Net model comprising an encoder and three decoders to predict three output classes corresponding to three different flow fields, respectively. This deep U-Net model estimates fluid flow fields by learning from preprocessed data, that is, interpolated features data.
- Lastly, we evaluate the proposed method by measuring the learning and testing loss metrics. The experimental results show the competition and promise of the proposed method with other baseline models on the same dataset.
2. Related Work
3. The Proposed Method
3.1. Data Generation and Preprocessing
3.1.1. Random Shape Generation and Numerical Resolution of the Naiver–Stokes Equation
3.1.2. Learning Features Generation
Algorithm 1: Interpolated Input and Output Features Generation |
input: x-coordinate x, y-coordinate y, horizontal velocity u, vertical velocity v, pressure p, width m, height n output: 2D array of horizontal mesh-grid , 2D array of vertical mesh-grid , object binary map , interpolated horizontal velocity , interpolated vertical velocity , interpolated pressure P 1 // Create two 1D array following x, y coordinates 2 3 4 // Generate 2D numpy arrays are horizontal and vertical of mesh-grids using and 5 6 // Generate obstacle binary mapping 7 8 9 10 11 12 13 14 15 // Generate output features 16 17 18 19 return |
3.2. The Proposed CFD Based Deep U-Net Model
3.3. Model Evaluation and Optimization
Algorithm 2: Deep U-Net-based CFD Prediction Model |
4. Experimental Results and Discussion
4.1. Effectiveness of Hyper-Parameters
4.2. Performance Evaluation and Comparison to Other Deep Learning Models
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
CFD | Computational Fluid Dynamic |
DNNs | Deep Neural Networks |
CNNs | Convolution Neural Networks |
LES | Large Eddy Simulation |
RANDS | Reynolds Averaged Navier–Stokes |
ROM | Reduced Order Model |
POP | Proper Orthogonal Decomposition |
DL | Deep Learning |
PDEs | Partial Different Equations |
AE | Autoencoder |
SDF | Signed Distance Function |
MCR | MATLAB Compiler Runtime |
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Kernel Size | Filter | Training Loss | Testing Loss | Ux’s MSE | Uy’s MSE | P’s MSE |
---|---|---|---|---|---|---|
(4, 8, 16, 16) | 8.043 | 8.585 | 4.740 | 3.465 | 0.379 | |
5 | (8, 16, 32, 32) | 15.556 | 17.438 | 14.349 | 1.795 | 1.293 |
(16, 32, 64, 64) | 3.473 | 3.069 | 2.066 | 0.602 | 0.400 | |
(4, 8, 16, 16) | 3.016 | 3.315 | 2.531 | 0.711 | 0.073 | |
11 | (8, 16, 32, 32) | 3.016 | 3.315 | 2.531 | 0.711 | 0.073 |
(16, 32, 64, 64) | 0.309 | 0.452 | 0.404 | 0.033 | 0.014 |
Obstacle | Train Loss | Test Loss | Ux’s MSE | Uy’s MSE | P’s MSE |
---|---|---|---|---|---|
Triangle | 0.524 | 1.198 | 0.903 | 0.236 | 0.058 |
Rectangle | 0.541 | 3.366 | 3.366 | 0.081 | 0.253 |
Pentagon | 3.255 | 4.855 | 3.559 | 0.474 | 0.821 |
Model | Training Loss | Testing Loss | Ux’s MSE | Uy’s MSE | P’s MSE |
---|---|---|---|---|---|
AE | 11.183 | 11.183 | 12.688 | 1.125 | 1.408 |
Single U-Net | 4.599 | 5.017 | 1.127 | 3.861 | 0.027 |
Proposed method | 0.335 | 0.345 | 0.294 | 0.294 | 0.015 |
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Le, T.-T.-H.; Kang, H.; Kim, H. Towards Incompressible Laminar Flow Estimation Based on Interpolated Feature Generation and Deep Learning. Sustainability 2022, 14, 11996. https://doi.org/10.3390/su141911996
Le T-T-H, Kang H, Kim H. Towards Incompressible Laminar Flow Estimation Based on Interpolated Feature Generation and Deep Learning. Sustainability. 2022; 14(19):11996. https://doi.org/10.3390/su141911996
Chicago/Turabian StyleLe, Thi-Thu-Huong, Hyoeun Kang, and Howon Kim. 2022. "Towards Incompressible Laminar Flow Estimation Based on Interpolated Feature Generation and Deep Learning" Sustainability 14, no. 19: 11996. https://doi.org/10.3390/su141911996