Evaluating the fast method based on proper orthogonal decomposition for radiative heat transfer in a participating medium

Document Type : Research Article

Authors

1 Department of Mechanical Engineering, Faculty of Engineering, University of Birjand, Birjand, Iran

2 Department of Mechanical Engineering, Faculty of Engineering, University of Qom, Qom, Iran

Abstract

The radiative transfer equation models the thermal radiation in a participating medium. Except in specified cases, there is no analytical solution for this equation. Solving the radiative transfer equation with numerical methods is usually time-consuming. This work presents a fast method based on proper orthogonal decomposition to solve the radiative transfer equation. Some variables are selected as independent parameters. The radiative transfer equation for the specified value of these parameters is solved using the discrete ordinates method, and the system responses form the snapshot matrix. The matrix is decomposed singular value decomposition as a product of three matrices. Due to the magnitude of singular values, only a few first columns of these matrices are selected. As a result, the degrees of freedom of the original system are decreased, and a reduced-order model is created. Employing the radial basis functions, the system response, corresponding to any arbitrary input vector (independent parameters), can be approximated with high speed. The results show that the reduced-order method has high accuracy compared to the numerical solution. The complexities of the system do not affect the reduced-order method. Regardless of the characteristics of the medium (the value of independent parameters), the solution time is the order of 0.02 seconds.

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Main Subjects

References

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Amirkabir Journal of Mechanical Engineering
Volume 54, Issue 9
December 2022
Pages 2175-2174

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