Development of Parametric and Time-Dependent Reduced Order Model for Diffusion and Convection-Diffusion Problems Based on Proper Orthogonal Decomposition

Numerical modeling and simulation is a useful tool for analyzing the dynamic behavior of engineering systems. Using these methods, especially for unsteady problems, usually requires a lot of time. For this reason, the development of fast speed algorithms and increased computational efficiency has always been an important issue for researchers. In this method, by decreasing the constraints of the system, the computational speed will dramatically increase without changing the dominant features of the problems. In this research, using the basic concepts of dynamical systems, two problems such as diffusion and convection-diffusion of equations are investigated independently and by using the proper orthogonal decomposition method, the reduced-order model for these equations have been created. Finally, for each of the problems, based on the projection of the related governing equations in the vector space of modes and using more energetic modes, a reduced-order model is obtained with respect to the orthogonal basis functions. The model obtained has been used to simulate the time evolutions of each problem. These equations can correctly replace with the primary equation and predict the behavior of the system with very good accuracy. Comparison of the results of the reduced-order model and direct numerical simulation shows high accuracy.