Physics-Informed Data-driven Reduced Order Model of the Convection-Diffusion Equation Using Dynamic Mode Decomposition

Articles in Press

Document Type : Original Article

Authors

1 Department of Mechanical Engineering, University of Qom

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

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 will 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 to a reduced-order model. The results show 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 is decreased. 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 the eddy viscosity concept, an attempt has been 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 the 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

Soft Computing Journal

Articles in Press, Accepted Manuscript
Available Online from 23 July 2024

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History

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

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