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Discontinuous 1-D Spherical Transport Solvers using Diffusion Preconditioner and Iterative Methods

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Abstract

Using discontinuous Galerkin finite-element methods to solve the hyperbolic components of the transport operator in the 1-D spherically symmetric case, the convergence behavior of various iterative methods are compared and evaluated. Diffusion synthetic accelerator, a preconditioner based on the diffusion approximation to the transport equation, is presented formally for this geometry for the first time. Compared with classical, finite-difference like methods (diamond difference methods), it is found that DG diffusion based preconditioners performed extremely well in resolving problems with strong scattering effects and material discontinuities.

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  1. National Security Technologies, LLC, P.O. Box 98521, M/S NLV 070, Las Vegas, NV, 89193-8521, USA

    Eric Machorro

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  1. Eric Machorro
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Correspondence to Eric Machorro.

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This manuscript has been authored by National Security Technologies, LLC, under Contract No. DE-AC52-06NA25946 with the US Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. STP Rev. DOE/NV/25946-594.

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Machorro, E. Discontinuous 1-D Spherical Transport Solvers using Diffusion Preconditioner and Iterative Methods. J Fusion Energ 31, 325–340 (2012). https://doi.org/10.1007/s10894-011-9460-x

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