Skip to main content
Open Access Publications from the University of California

UC Merced

UC Merced Previously Published Works bannerUC Merced

Advanced differential approximation formulation of the PN method for radiative transfer

  • Author(s): Pal, G
  • Modest, MF
  • et al.

Published Web Location

The spherical harmonics (P ) method, especially its lowest order, i.e., the P1 or differential approximation, enjoys great popularity because of its relative simplicity and compatibility with standard models for the solution of the (overall) energy equation. Low-order PN approximations perform poorly in the presence of strongly nonisotropic intensity distributions, especially in optically thin situations within nonisothermal enclosures (due to variation in surface radiosities across the enclosure surface, causing rapid change of irradiation over incoming directions). A previous modification of the PN approximation, i.e., the modified differential approximation (MDA), separates wall emission from medium emission to reduce the nonisotropy of intensity. Although successful, the major drawback of this method is that the intensity at the walls is set to zero into outward directions, while incoming intensity is nonzero, resulting in a discontinuity at grazing angles. To alleviate this problem, a new approach, termed here the advanced differential approximation (ADA)is developed, in which the directional gradient of the intensity at the wall is minimized. This makes the intensity distribution continuous for the P1 method and mostly continuous for higher-order PN methods. The new method is tested for a 1D slab and concentric spheres and for a 2D medium. Results are compared with the exact analytical solutions for the 1D slab as well as the Monte Carlo-based simulations for 2D media. N

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.

Main Content
Current View