High resolution time integration for SN radiation transport |
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Authors: | Greg Thoreson Ryan G. McClarren Jae H. Chang |
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Affiliation: | 1. Nuclear Engineering Teaching Lab, University of Texas, Austin, TX 78712, USA;2. Computational Physics and Methods Group (CCS-2), Los Alamos National Laboratory, Los Alamos, NM 87545, USA |
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Abstract: | First-order, second-order, and high resolution time discretization schemes are implemented and studied for the discrete ordinates (SN) equations. The high resolution method employs a rate of convergence better than first-order, but also suppresses artificial oscillations introduced by second-order schemes in hyperbolic partial differential equations. The high resolution method achieves these properties by nonlinearly adapting the time stencil to use a first-order method in regions where oscillations could be created. We employ a quasi-linear solution scheme to solve the nonlinear equations that arise from the high resolution method. All three methods were compared for accuracy and convergence rates. For non-absorbing problems, both second-order and high resolution converged to the same solution as the first-order with better convergence rates. High resolution is more accurate than first-order and matches or exceeds the second-order method. |
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