Modified discrete ordinates and finite volume methods

The discrete ordinates method (DOM) and the finite volume method (FVM) suffer from ray effects, as discussed in the article “Ray Effects and False Scattering”. Ray effects may be successfully reduced by increasing the number of discrete directions in the DOM or the number of control angles in the FVM. However, ray effects decrease slowly with the refinement of the angular quadrature. The modified discrete ordinates method, MDOM (Ramankutty and Crosbie, 1997), based on the modified differential approximation (Olfe, 1970, Modest, 1989), proved to significantly mitigate ray effects originated from discontinuities or abrupt changes of the wall temperature. The model was originally developed for two-dimensional enclosures with black walls and homogeneous, isotropi ...