Stabilized DMD based reduced-order model of the convection-diffusion equations at high Reynolds numbers using the eddy viscosity closure

Because analytical methods are less commonly used due to their low accuracy and limited application range, and numerical methods are time-consuming and have computer hardware limitations, especially in unsteady problems, researchers The development of models and solution methods has turned to higher speeds and efficiencies. One of these patterns is the order reduction method. The reduced rating method is an alternative model for simulating flow dynamics. Degraded models are developed mainly on the basis of calculating the effective structures of a dynamic system. The dynamic mode Decomposition method is one of the methods for calculating these basic structures. Using this model and using the principles of dynamic systems, the viscous Burgers equation has been transformed into a low-ranking dynamic system. If the Reynolds number is increased and the effects of the viscous term in the governing equation are reduced, the depreciation required in the system to stabilize the numerical solution is reduced. Also, due to the incompleteness of the assumed modes in the problem and the elimination of the effect of modes with higher numbers, this decrease in depreciation will be more pronounced. Therefore, by creating an artificial loss called vortex viscosity, an attempt is made to stabilize the system. Finally, by comparing the results obtained from the reduced model and direct numerical simulation results, the accuracy of this model is proven.