Dots: Pseudo-time-stepping solution of the discrete ordinate equations

The Discrete Ordinates with Time Stepping (DOTS) numerical solution method for the general discrete ordinates approximation of the radiative transport equation is presented. A pseudo-time iteration is employed, with simultaneous updating of all ordinates in each sweep. This may be beneficial for cases with strong scattering and therefore strong coupling between ordinate directions. The iteration is guaranteed to converge, subject to a stability criterion similar to the Courant-Friedrichs-Lewy stability condition. The DOTS algorithm was implemented for general three-dimensional geometry, boundary conditions, and medium properties. Convergence rates were significantly improved by including a multigrid process. We demonstrate the validity of the code on benchmark cases. The methods and implementation are compatible with mainstream computational fluid dynamics practices, and can be easily integrated with existing CFD codes.