عنوان مقاله [English]
Simulation and numerical analysis of physical phenomena, especially for the unsteady problems due to the dependency of the numerical algorithms on the computer hardware and the large number of computational nodes, are the most important problems. For these reasons, the number of computations and computational costs increase. The order reduction method is the one that has been widely used in recent years to reduce computational time. In this way, by reducing the constraints of the system without changing the inherent features of the problem, the computational efficiency will dramatically increase. In this study, using the basic concepts of dynamical systems, the thermal diffusion problem is investigated using the dynamic modes decomposition method. Then, a reduced order model is established for the related governing equation of this phenomenon. Accordingly, based on the projection of the governing equation in the vector space of modes, by using dynamic modes, a reduced order model is obtained with respect to the properties of dynamic modes. The obtained model to simulate the time evolution and parametric variations can be properly replaced with the original equation and predict the behavior of the system with very good accuracy. A comparison between the results of the present reduced order models and the simulations of the exact solution shows high computation accuracy.