A nonlinear acceleration method for radiative transfer problems
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Copyright (2015) by the American Nuclear Society All rights reserved. We present thermal radiation-transport solution techniques that use gray (one-group) diffusion low-order equations to speed iterative convergence. In the Gray Diffusion Acceleration (GDA) method, a diffusion adaptation of Larsen's Gray Transport Acceleration (GTA), a gray diffusion equation is used to accelerate or precondition linear iterations for the absorption-rate density (ARD). In the nonlinear GDA method, a gray diffusion equation is coupled to the temperature equation and used with a modified Newton's method to generate new iterates for both temperature and ARD. We discuss theoretical considerations and present results from test problems that include Marshak waves and the well-known "tophat" problem. We find that the effectiveness of a gray preconditioner degrades as the variance of the opacity across energy groups grows. We also find that the nonlinear acceleration method is effective for well behaved opacities, significantly reducing the number of transport sweeps relative to the linear preconditioning approach.
