An intelligent optimization method for accelerating physical quantity reconstruction in computational fluid dynamics

Shanpu Gao; Yubo Li; Anping Wu; Hao Jiang; Feng Liu; Xinlong Feng; Shanpu Gao; Yubo Li; Anping Wu; Hao Jiang; Feng Liu; Xinlong Feng

doi:10.3934/era.2025127

Electronic Research Archive

2025, Volume 33, Issue 5: 2881-2924. doi: 10.3934/era.2025127

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An intelligent optimization method for accelerating physical quantity reconstruction in computational fluid dynamics

1.
College of Mathematics and System Sciences & Institute of Mathematics and Physics, Xinjiang University, Urumqi 830046, China
2.
Hypervelocity Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang 621000, China
3.
National Key Laboratory of Aerospace Physics in Fluids, Mianyang 621000, China
4.
School of Computer Science and Technology, Southwest University of Science and Technology, Mianyang 621010, China

Received: 13 February 2025 Revised: 02 April 2025 Accepted: 17 April 2025 Published: 13 May 2025

The weighted essentially non-oscillatory (WENO) scheme is widely used in fluid mechanics and other numerical simulation fields because of its high precision and low oscillation characteristics when dealing with hyperbolic conservation law equations containing discontinuities and high-gradient regions. However, the calculation of nonlinear weights in the WENO reconstruction process is complex and entails a high computational cost, especially when addressing two-dimensional and higher-dimensional problems, resulting in a limited overall computational efficiency. To improve computational efficiency, this study introduces a novel neural network-enhanced weighted essentially non-oscillatory method, abbreviated as WENO-NN. This method replaces the reconstruction process in the WENO scheme. Specifically, we used a subset of the data generated by the WENO method to train a neural network that approximates the functionality of WENO. This approach significantly improved the computational efficiency while preserving accuracy. Further, we evaluated the performance of the WENO-NN scheme on both one-dimensional, two-dimensional, and three-dimensional test cases, including scenarios involving the interaction of strong shocks and shock-density waves. The results demonstrated that the WENO-NN scheme exhibits good versatility across all benchmark tests and resolutions. Its accuracy is comparable to that of the classic WENO scheme, while its computational efficiency is improved by 3 times.
- WENO-NN,
- neural network,
- WENO,
- acceleration algorithm
Citation: Shanpu Gao, Yubo Li, Anping Wu, Hao Jiang, Feng Liu, Xinlong Feng. An intelligent optimization method for accelerating physical quantity reconstruction in computational fluid dynamics[J]. Electronic Research Archive, 2025, 33(5): 2881-2924. doi: 10.3934/era.2025127

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Abstract

The weighted essentially non-oscillatory (WENO) scheme is widely used in fluid mechanics and other numerical simulation fields because of its high precision and low oscillation characteristics when dealing with hyperbolic conservation law equations containing discontinuities and high-gradient regions. However, the calculation of nonlinear weights in the WENO reconstruction process is complex and entails a high computational cost, especially when addressing two-dimensional and higher-dimensional problems, resulting in a limited overall computational efficiency. To improve computational efficiency, this study introduces a novel neural network-enhanced weighted essentially non-oscillatory method, abbreviated as WENO-NN. This method replaces the reconstruction process in the WENO scheme. Specifically, we used a subset of the data generated by the WENO method to train a neural network that approximates the functionality of WENO. This approach significantly improved the computational efficiency while preserving accuracy. Further, we evaluated the performance of the WENO-NN scheme on both one-dimensional, two-dimensional, and three-dimensional test cases, including scenarios involving the interaction of strong shocks and shock-density waves. The results demonstrated that the WENO-NN scheme exhibits good versatility across all benchmark tests and resolutions. Its accuracy is comparable to that of the classic WENO scheme, while its computational efficiency is improved by 3 times.

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