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 simultane ous updating of all ordinates in each sweep. This may be beneficial for cas es with strong scattering and therefore strong coupling between ordinate di rections. The iteration is guaranteed to converge, subject to a stability c riterion similar to the Courant-Friedrichs-Lewy stability condition. The DO TS algorithm was implemented for general three-dimensional geometry, bounda ry conditions, and medium properties. Convergence rates were significantly improved by including a multigrid process. We demonstrate the validity of t he code on benchmark cases. The methods and implementation are compatible w ith mainstream computational fluid dynamics practices, and can be easily in tegrated with existing CFD codes.