Development of parametric and time dependent reduced order model for diffusion and convection-diffusion problems based on proper orthogonal decomposition method

Document Type : Research Article

Authors

1 Department of Mechanical Engineering, University of Qom

2 Department of Mechanical Eng. Univ. Qom

Abstract

Simulation and numerical analysis of physical phenomena, especially for unstable problems, due to dependency of the numerical algorithms on the computer hardware to the increasing of the number of computational nodes, is the most important feature of their solutions. For this reason, increases the number of computations then increased computational costs. The order reduction method 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, two problems of thermal diffusion and convection-diffusion are investigated independently and by using the proper orthogonal analysis method, a reduced order model is established for the equations governing these phenomena created. Accordingly, for each of the problems, based on the projection of the governing equation in the vector space of modes, by using more energetic modes, a reduced order model is obtained with respect to the orthogonal basis properties. The model obtained in order to simulate the process time variations can properly replace the original equation and predict the behavior of the system with very good accuracy.

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References

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Amirkabir Journal of Mechanical Engineering
Volume 53, Issue 7
October 2021
Pages 4241-4260

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