Iranian Journal of Mechanical Engineering Transactions of the ISME

Iranian Journal of Mechanical Engineering Transactions of the ISME

Stabilization of Intrusive DMD based Reduced Order Model of the Convection-diffusion Equations

Document Type : Research Paper

Authors
Mohammad Kazem Moayyedi
Fatemeh Bigdeloo
Zohreh Khakzari
CFD Turbulence and Combustion Research Lab., Department of Mechanical Engineering, University of Qom, Qom, Iran / Institute of Aerospace Studies, University of Qom, Qom, Iran
10.30506/jmee.2024.2007857.1317
Abstract
Simulation of complex and non-linear dynamical systems needs numerical algorithms which are time-consuming due to hardware limitations. Therefore, many studies were focused on developing models with high speed of computation and good relative accuracy. Reduced-order model is the method that could be an alternative approach for simulating complex dynamical systems using some appropriate data from the system responses. Usually, these models are developed based on the dominant features of the desired system. Dynamic Mode Decomposition is one of the methods for calculating these basis functions. In this study, using this method and based on the concepts of dynamical systems, a reduced-order model has been developed for Burgers equation. Also, due to the incompleteness of the related modal space which is changed to low-dimensional space in order reduction procedure, the dissipation level of the surrogate model is decreased. Therefore, by using an artificial viscosity which is called the eddy viscosity approach, the stability of the model is improved. Eventually, comparing the results obtained by the stabilized reduced order model and direct numerical simulation data, the accuracy of the model with an average error of 0.4% is proven.
Keywords
Dynamic Mode Decomposition (DMD)
Reduced order model
Eddy viscosity approach
Burgers equation
Stabilization approach
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