Efficient Calculation of Radiation Heat Transfer in Participating Media

Abstract

A low-cost computational solution to radiation problems can be obtained by using a simple model, such as the P 1 model, but the accuracy can be very poor. High accuracy can be obtained by solving the radiative transfer equation, but the solution cost can be exorbitant for strongly participating media. The Q L method presented in this paper allows the radiation heat transfer to be computed from a single equation for the average intensity, like the P 1 model, but the Q L equation contains parameters that account for a nonuniform intensity distribution. The method converges to the solution of the radiative transfer equation with grid refinement and will accommodate any scattering phase function. For a given spatial and directional discretization, and for problems involving radiation only, the accuracy of the Q L method is shown to equal or exceed that of the finite volume method. The solution cost of the Q L method is comparable to the finite volume method for weakly participating media, but for strongly participating media the Q L method is much less costly. The Q L method is designed for application in general-purpose codes in which radiation is but one of several important processes, and it is in such applications that the major benefits of the Q L method are expected.