Ray Effects and False Scattering in Improved Discrete Ordinates Method

The improved discrete ordinates method (IDOM) developed in our previous paper is extended to solve radiative transfer in three-dimensional radiative systems with anisotropic scattering medium. In IDOM, radiative intensities in a large number of new discrete directions are calculated by direct integration of the conventional discrete ordinates method (DOM) results, and radiative heat flux is obtained by integrating radiative intensities in these new discrete directions. Ray effects and false scattering, which tend to compensate each other, are investigated together in IDOM. Results show that IDOM can mitigate both of them effectively with high computation efficiency. Finally, the effect of scattering phase function on radiative transfer is studied. Results of radiative heat flux at boundaries containing media with different scattering phase functions are compared and analyzed. This paper indicates that the IDOM can overcome the shortages of the conventional DOM well while inheriting its advantages such as high computation efficiency and easy implementation.

ANALYTIC DISCRETE-ORDINATES SOLUTION FOR TIME-DEPENDENT TRANSPORT IN FINITE MEDIA

We present an extension of the Analytic Discrete-Ordinates method to time-dependent transport in finite media. The application of this technique to time-dependent transport is primarily accomplished through the use of a Laplace transform. In the case of finite media, a system of equations arises from enforcing boundary conditions. Instead of directly solving this system, we construct a solution in terms of a Neumann series. We then show that terms can be neglected when numerically evaluating the inverse Laplace transform such that the series reduces to a finite sum. With this extension, we use convergence acceleration to generate a high-precision benchmark.