Enhanced discrete ordinates approach for mitigating shadowing effects in obstructed gas-filled spaces: Implications for astrophysical and industrial applications

This article introduces a novel quadrature scheme for the discrete ordinates method (DOM) called Uniform Constant Weight Quadrature (UCWQ). A new version of the discrete ordinates method has been developed to address the shadowing effects in gas-filled enclosures with obstructions. The UCWQ method*, featuring a novel pyramidal mesh within the quadrature set, meets the criteria for the zeroth, first, and second moments and is symmetric to any axis. In comparison to the standard SN quadrature, the UCWQ method allows for unlimited angular refinement, thereby preventing distortions in temperature and radiative flux profiles caused by shadowing effects. The new scheme demonstrates high performance in calculating the radiative propagation through a semi-transparent medium situated between two concentric spheres. This new technique can be easily adopted to study a wide range of industrial applications, as well as various astrophysical systems, such as stellar atmospheres and structures within the interstellar medium. It can also be used to study the radiation contribution of greenhouse gases in atmospheric pollution layers.