A computationally efficient P1 radiation model for modern combustion systems utilizing pre-conditioned conjugate gradient methods

Abstract

The iterative convergence of the P1 radiation model can be slow in optically thin scenarios when employing classical iterative methods. In order to remedy this shortcoming, an in-house P1 radiation model was interfaced with high performance, scalable, linear solver libraries. Next, the accuracies of P1 radiation model calculations was assessed by comparing its predictions against discrete ordinates (DO) model calculations for prototypical problems representative of modern combustion systems. Corresponding benchmark results were also included for comparison.Utilizing Pre-Conditioners (PC) to the Conjugate Gradients (CG) method, the convergence time of the P1 radiation model reduced by a factor of 30 for modest problem sizes and a factor of 70 for larger sized problems when compared against classical Gauss Seidel sweeps. Further, PC provided 50% computational savings compared to employing CG in a standalone mode. The P1 model calculation times were about 25–30% of the DO model calculation time. The time to solution also scaled linearly with an increase in problem size. The weighted sum of gray gases model employed in this study in conjunction with the P1 model provided good agreement against benchmark data with L2 error norms (defined relative to corresponding DO calculations) improving when isotropic intensities were prevalent.