Efficient calculation of radiation heat transfer in participating media

A low-cost computational solution to radiation problems can be obtained by using a simple model, such as the P, 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.