A modified differential approximation proposed by Olfe is extended to the treatment of a medium with isotropic scattering and boundary reflection. The method can be used to readily generate successive improvement of the solutions. In this work, the basic procedure is demonstrated by computing the transmissivity and hemispherical reflectivity of an absorbing, isotropically scattering slab with a reflecting boundary. Comparison of present computational results with existing exact solutions shows that, in general, the modified differential approximation is superior to the unmodified differential approximation, and that one or two applications of the improvement of the modified differential approximation produces results very close to the exact solution. The present method also gives accurate solutions for an optically-thin medium. The general concept of the current method appears to be adaptable to the treatment of multidimensional cases.
All Science Journal Classification (ASJC) codes
- Condensed Matter Physics
- Aerospace Engineering
- Mechanical Engineering
- Fluid Flow and Transfer Processes
- Space and Planetary Science