Studying the Effect of Eddy Viscosity Closure on the Calibration of the DMD based Reduced-order Model to Predict the Long-term Behavior of Convection-Diffusion Equations

In this research, using the dynamic modes decomposition and using the basic concepts of the dynamical system, a data driven-physics informed reduced-order model has been developed for the viscous Burgers equation. Accordingly, based on the projection of the governing equation into the modal space, a reduced model is obtained according to the characteristics of the dominant modes. This model when used to simulate the field dynamics over a long time period, may become unstable. Therefore, an approach based on the concept of eddy viscosity closure has been used to stabilize the model behavior. This modification allows the reduced-order model to be a surrogate model of the original equation and predict the time evolution of the dynamical system with relative good accuracy. Comparing the results of the present reduced order model with the data obtained from the direct numerical simulations shows a high computational accuracy.