A discontinuous Galerkin Method based on POD model reduction for Euler equation

Lan Zhu; Li Xu; Jun-Hui Yin; Shu-Cheng Huang; Bin Li; Lan Zhu; Li Xu; Jun-Hui Yin; Shu-Cheng Huang; Bin Li

doi:10.3934/nhm.2024004

Networks and Heterogeneous Media

2024, Volume 19, Issue 1: 86-105. doi: 10.3934/nhm.2024004

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Research article

A discontinuous Galerkin Method based on POD model reduction for Euler equation

1.
National Key Laboratory of Science and Technology on Vacuum Electronics, School of Electronic Science and Engineering, University of Electronic Science and Technology of China, Chengdu, China
2.
Shenzhen Institute for Advanced Study, UESTC Yinxing Zhijie Phase Ⅱ, Guanlan Street, Longhua District, Shenzhen, China

Received: 25 July 2023 Revised: 29 November 2023 Accepted: 20 December 2023 Published: 15 January 2024

This paper considers the work of combining the proper orthogonal decomposition (POD) reduced-order method with the discontinuous Galerkin (DG) method to solve three-dimensional time-domain Euler equations. The POD-DG formulation is established by constructing the POD base vector space, based on POD technology one can apply the Galerkin projection of the DG scheme to this dimension reduction space for calculation. Its overall goal is to overcome the disadvantages of high computational cost and memory requirement in the DG algorithm, reduce the degrees of freedom (DOFs) of the calculation model, and save the calculation time while ensuring acceptable accuracy. Numerical experiments verify these advantages of the proposed POD-DG method.
- computational fluid dynamics,
- Euler equations,
- discontinuous Galerkin method,
- proper orthogonal decomposition,
- model reduction method
Citation: Lan Zhu, Li Xu, Jun-Hui Yin, Shu-Cheng Huang, Bin Li. A discontinuous Galerkin Method based on POD model reduction for Euler equation[J]. Networks and Heterogeneous Media, 2024, 19(1): 86-105. doi: 10.3934/nhm.2024004

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Abstract

This paper considers the work of combining the proper orthogonal decomposition (POD) reduced-order method with the discontinuous Galerkin (DG) method to solve three-dimensional time-domain Euler equations. The POD-DG formulation is established by constructing the POD base vector space, based on POD technology one can apply the Galerkin projection of the DG scheme to this dimension reduction space for calculation. Its overall goal is to overcome the disadvantages of high computational cost and memory requirement in the DG algorithm, reduce the degrees of freedom (DOFs) of the calculation model, and save the calculation time while ensuring acceptable accuracy. Numerical experiments verify these advantages of the proposed POD-DG method.

References

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