A multi-source full spectrum k-distribution method for 1-D inhomogeneous media

- k-Distribution based approach yields line-by-line accurate solution to inhomogeneous problems with piecewise constant temperature and property distributions.
- MSFSK solutions are considerably less computationally expensive than line-by-line solutions.
- Approximating a temperature and property distributions as piecewise constant introduces well-known and quantifiable errors.

The k-distribution method for treating the spectral properties of an absorbing-emitting medium represents an alternative to line-by-line calculations. It reduces the number of RTE evaluations from the order of a million to the order of ten without any significant loss of accuracy. For problems where an appropriate reference temperature can be defined, the k-distribution method is formally exact. However, when no appropriate reference temperature can be defined, the method results in errors. There have been several attempts to implement corrections to the k-distribution method to extend its application to inhomogeneous media by modeling the effects of temperature, pressure, and concentration gradient. Some of these techniques are effective at reducing these errors, but none successfully extend the k-distribution method to inhomogeneous media in a way that retains the analytical guarantee of line-by-line accuracy. The Multi-Source Full Spectrum K-Distribution Method (MSFSK) introduced here manages to attain this goal for 1-dimensional domains with piecewise constant temperature distributions by applying the superposition principle to the original RTE before applying the k-distribution transformation to decompose the problem into a set of sub-problems each of which is able to be solved exactly via the ordinary or modified full spectrum k-distribution method.