The DOM approach to the collapsed dimension method for solving radiative transport problems with participating media

A new formulation of the collapsed dimension method (CDM), called the modified collapsed dimension method (MCDM) whose approach is similar to the discrete ordinate method (DOM), has been proposed. In the MCDM, the time consuming procedures of ray tracing and source term evaluation are not required, as a result of which the method becomes computationally efficient. To validate the formulation, test problems dealing with radiative heat transfer with absorbing, emitting and scattering medium have been considered. To compare the performance of the MCDM, the same problems have also been solved using the CDM and the DOM. Results have been compared against the benchmark results. For the same level of accuracy, MCDM has been found faster than the CDM and the DOM. However, the number of iterations required for the converged solution in the MCDM and the DOM has been found to be almost the same.