Evaluation of a fast method based on proper orthogonal decomposition to survey the radiative heat transfer in a participating media

To survey the radiative heat transfer in a participating medium, the radiative transfer equation must be solved. Except in particular cases, there is no analytical solution to it. Solving the RTE with numerical methods is also time consuming. In combined conductive-radiative or convective-radiative heat transfer, and inverse heat transfer problems, the RTE must be solved several times; Therefore, the computation time will be momentous. In this work, a fast method based on proper orthogonal decomposition to solve the RTE is presented. A number of properties (such as: emissivity, absorption and scattering coefficients) are selected as independent parameters. The RTE for specified modes of these parameters is solved using the discrete ordinates method, and the system responses form the snapshot matrix. Using the singular value decomposotion, it is decomposed. According to the singular values, only certain columns of the matrices are selected. As a result, the degrees of freedom of the system are reduced, and a reduced-order model is created. Employing the radial basis functions, the system response can be predicted rapidly for any desired input vector (including independent parameters). The results show that the ROM has a high accuracy compared to the DOM results. The complexities of the system have no effect on the CPU Time, and regardless of the value of the independent parameters, the computation time is of the order of 0.02 seconds.