A direct collocation meshless approach with upwind scheme for radiative transfer in strongly inhomogeneous media

- An upwind collocation meshless (UPCM) method is first developed to solve the RTE.
- Complex enclosures with strongly inhomogeneous participating media are considered.
- The trial function is constructed by a moving least-squares (MLS) approximation.
- The computational accuracy, stability, and efficiency of the UPCM method are analyzed.
- UPCM is more accurate than the meshless method based on SORTE in some cases.

A direct collocation meshless (DCM) method with upwind scheme is employed for solving the radiative transfer equation (RTE) for strongly inhomogeneous media. The trial function is constructed by a moving least-squares (MLS) approximation. The upwind scheme is implemented by moving the support domain of MLS approximation to the opposite direction of each streamline. To test computational accuracy and efficiency of the upwind direct collocation meshless (named UPCM) method, various problems in 1-D and 2-D geometries are analyzed. For the comparison, we also present cases of both the DCM method for the first-order RTE (employed by Tan et al. [1]) and the DCM for the MSORTE (a new second-order form of radiative transfer equation proposed by Zhao et al. [2]). The results show that the proposed method is more accurate and stable than the DCM method (no upwinding) based on both the RTE and MSORTE. Computationally, it is also faster.