A fast method based on Dynamic Mode Decomposition for radiative heat transfer in participating media. (September 2022) - Sharak, M. Niknam; Safavinejad, A.; Moayyedi, M.K.
Highlights: A fast method based on dynamic mode decomposition (DMD) is introduced for solving the radiative transfer equation (RTE) in an absorbing-emitting and scattering medium. Complex numerical methods in solving the RTE, such as discrete ordinates method (DOM), become a simple matrix multiplication. The DMD method, commonly used for dynamic transient problems, is used to reduce the order of the radiative heat transfer, which is a time-independent problem. The RTE computation time, which in conventional numerical methods is from the order of 100 seconds, is reduced to a time of the order of 0.01 seconds. The radiative properties of the participating medium strongly influence the computational cost. But in the present method, the complexities of the problem do not affect the computation time, and the it is always of the order of 0.01 seconds. Abstract: The radiative transfer equation (RTE) is an integro-differential equation and solving it is time-consuming except in a few specific cases. A fast method based on dynamic mode decomposition (DMD) is introduced for solving the RTE in an absorbing-emitting and scattering medium. First, some parameters are considered as independent variables. The RTE is solved for different values of these parameters (known input vectors) using the discrete ordinates method ( S 6 approximation), and the system responses generate the snapshot matrix. Then using the DMD technique, the dynamic modes are constructed, so the degree of freedom of the system is decreased. The reduced-order model (ROM), called DMD-RBF, is generated by combining the DMD and the radial basis functions. Two cases, radiative equilibrium and medium with known temperature (isothermal and non-isothermal), are considered. The accuracy of the model is investigated using random input vectors. The results show that the DMD-RBF has a good agreement with the numerical solutions. Comparison between the ROM and numerical CPU times shows the high efficiency of the ROM. The results also show that the problem complexity does not affect the computational cost. For all cases, the CPU time of the ROM is of the order of 0.01 seconds.