Nonlinear Diffusion Synthetic Acceleration Difference Schemes for Radiative Transfer Applications

A new three-point nonlinear difference scheme for diffusion synthetic acceleration (DSA) of the radiation transport equation is described. The new scheme is compared with the standard one-point method on two test problems. In addition, the two DSA methods are used to accelerate a variety of discrete ordinates difference schemes. The methods are very effective in accelerating the convergence of the transport iteration. Each of the DSA methods is accelerated by grey, or one-group, diffusion acceleration equation, which is also successful in increasing efficiency. The new method is at least 50% faster than one-point DSA method and this advantage increases with the difficulty of the problem and with tighter convergence criteria. The new acceleration method reduces computer time by at least one order of magnitude compared to unaccelerated calculations.