Reduced Order Model for Boundary Instigation of Burgers’ Equation of Turbulence Using Direct and Indirect Control Approaches

Document Type : Research Article

Author

Department of Mechanical Engineering, University of Qom

Abstract

In this paper, a reduced order model is reconstructed for boundary control and excitation of the unsteady viscous Burger's equation. First, the standard reduced order POD model, which has been extracted from the governing equations without control inputs, was evaluated and illustrated the satisfactory results in short time period. Two approaches are used to imply the effects of boundaries excitations and the related control routines. In the first, a source term was added to the governing equation of the reduced order dynamical system and was contributed as an expansion of the POD modes without control input. For removing the inhomogeneities on the boundaries, the boundaries values are subtracted from all of the snapshots with an appropriate control input. The other approach is based on the rewriting of the diffusion term as an expanded form which contains the effect of boundaries values explicitly. In both approaches, the obtained reduced order models will contain two parts, the effect of system states and the influence of boundaries control functions. The results obtained from the reduced order model without the control inputs demonstrate a good agreement to the benchmark DNS data and prove the high accuracy of the model. The results obtained from the reduced order model without the control inputs demonstrate a good agreement to the benchmark DNS data and prove the high accuracy of the model.

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