Publications
The impact of reference frame orientation on discrete ordinates solutions in the presence of ray effects and a related mitigation technique
The discrete ordinates method is a popular and versatile technique for deterministically solving the radiative transport which governs the exchange of radiant energy within a fluid or gas mixture. It is the most common 'high fidelity' technique used to approximate the radiative contribution in combined-mode heat transfer applications. A major drawback of the discrete ordinates method is that the solution of the discretized equations may involve nonphysical oscillations due to the nature of the discretization in the angular space. These ray effects occur in a wide range of problems including those with steep temperature gradients either at the boundary or within the medium, discontinuities in the boundary emissivity due to the use of multiple materials or coatings, internal edges or corners in non-convex geometries, and many others. Mitigation of these ray effects either by increasing the number of ordinate directions or by filtering or smoothing the solution can yield significantly more accurate results and enhanced numerical stability for combined mode codes. When ray effects are present, the solution is seen to be highly dependent upon the relative orientation of the geometry and the global reference frame. This is an undesirable property. A novel ray effect mitigation technique is proposed. By averaging the computed solution for various orientations, the number of ordinate directions may be artificially increased in a trivially parallelizable way. This increases the frequency and decreases the amplitude of the ray effect oscillations. As the number of considered orientations increases a rotationally invariant solution is approached which is quite accurate. How accurate this solution is and how rapidly it is approached is problem dependent. Uncertainty in the smooth solution achieved after considering a relatively small number of orientations relative to the rotationally invariant solution may be quantified.