Stabilization of Reduced Order Model for Convection-Diffusion Problems Based on Dynamic Mode Decomposition at High Reynolds Numbers Using Eddy Viscosity Approach

Document Type : Research Article

Authors

1 CFD, Turbulence and Combustion Research Lab., Department of Mechanical Engineering, University of Qom, Iran

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

Abstract

Since the analytical methods have a low accuracy and numerical algorithms are time-consuming with hardware limitations, therefore researchers are interested to develop models with high speed and efficiency. The reduced order model is the method that could be an alternative approach for simulating dynamical systems. These models are mainly developed based on the calculation of the dynamical systems' effective structures. The dynamic mode decomposition method is one of the methods for calculating these basic structures. In this study, using this model and based on the principles of dynamical systems, a reduced order model has been developed for the Burgers equation. The results show that if the Reynolds number increases then the effects of the viscous term in the governing equation are decreased, accordingly the required dissipation of the system to stabilize the numerical solution is reduced. Also, due to the incompleteness of the modes which are selected in the order reduction procedure, the dissipation level of the surrogate model is reduced more. Therefore, by creating an artificial dissipation called the eddy viscosity approach, the stability of the model is enhanced. Finally, by comparing the results obtained from the reduced order model and direct numerical simulation, the accuracy of this model is proven.

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References

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Amirkabir Journal of Mechanical Engineering
Volume 54, Issue 11
February 2023
Pages 2479-2498

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