Physics-informed data-driven reduced order model of the convection-diffusion equation using dynamic decomposition

Document Type : Original Article

Authors

1 Institute of Aerospace Studies, University of Qom, Iran

2 Space Science and Earth Atmosphere Research Laboratory, Department of Mechanical Engineering, University of Qom, Iran

Abstract

In the numerical analysis of fluid mechanics problems, especially in high resolution simulation, the reduction of computational costs has always been of great importance. The use of reduced-order models, which increase the speed of computation by reducing the constraints of the original model, is a suitable surrogate model for the original governing equation. In this research, using dynamic mode decomposition and based on principles of dynamical systems, the governing equation has been converted into a reduced order model. The results show that if the Reynolds number increases and the effects of the viscous term in the governing equation are reduced, the necessary dissipation in the representative model to stabilize the numerical solution decreases. Also, due to the incompleteness of the modal space and removing the effects of some modes, the instability will be enhanced. Therefore, by using an artificial dissipation term based on eddy viscosity concept, an attempt was made to increase the stability of the reduced order model. A stabilized reduced-order model, which is learned using a snapshots ensemble obtained for a specified Reynolds number, is used to simulate the problem for different Reynolds numbers. Comparison between the results obtained by reduced-order model with the exact solution shows the ability and high accuracy of the model to predict the problem dynamics.

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Main Subjects

References

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Soft Computing Journal
Volume 13, Issue 2 - Serial Number 26
February 2025
Pages 216-232

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History

  • Receive Date: 01 October 2023
  • Revise Date: 05 November 2023
  • Accept Date: 26 January 2024

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