Improved Discrete Ordinates Method for Ray Effects Mitigation

A new and improved method based on the concept of discrete ordinates scheme with infinitely small weights $(DOS+ISW)$ is developed for modeling radiative heat transfer in three-dimensional participating media. To demonstrate the effectiveness of the method in mitigating ray effects, the ray effects caused by (1) abrupt step changes in the boundary conditions and (2) the stepwise variation of the medium emissive power are considered. In this work, angular quadrature sets with large number of discrete ordinate directions are chosen to mitigate ray effects while at the same time keeping the computational time increase to a minimum. Comparing with the conventional discrete ordinates method, the difference is that intensities in these directions are calculated by $DOS+ISW$ method. Intensity with fine directional resolution calculated by this method is validated by comparing with that of reverse Monte Carlo method. The large number of discrete ordinate directions used in the new method becomes computationally prohibitive in the conventional discrete ordinates method due to the increased computer memory and computation time requirements.