A Multigroup diffusion solver using pseudo transient continuation for a radiation-hydrodynamic code with patch-based AMR

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We present a scheme to solve the nonlinear multigroup radiation diffusion (MGD) equations. The method is incorporated into a massively parallel, multidimensional, Eulerian radiation-hydrodynamic code with adaptive mesh refinement (AMR). The patch-based AMR algorithm refines in both space and time creating a hierarchy of levels, coarsest to finest. The physics modules are time-advanced using operator splitting. On each level, separate 'level-solve' packages advance the modules. Our multigroup level-solve adapts an implicit procedure which leads to a two-step iterative scheme that alternates between elliptic solves for each group with intra-cell group coupling. For robustness, we introduce pseudo transient continuation ({Psi}tc). We ... continued below

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Shestakov, A I & Offner, S R September 21, 2006.

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We present a scheme to solve the nonlinear multigroup radiation diffusion (MGD) equations. The method is incorporated into a massively parallel, multidimensional, Eulerian radiation-hydrodynamic code with adaptive mesh refinement (AMR). The patch-based AMR algorithm refines in both space and time creating a hierarchy of levels, coarsest to finest. The physics modules are time-advanced using operator splitting. On each level, separate 'level-solve' packages advance the modules. Our multigroup level-solve adapts an implicit procedure which leads to a two-step iterative scheme that alternates between elliptic solves for each group with intra-cell group coupling. For robustness, we introduce pseudo transient continuation ({Psi}tc). We analyze the magnitude of the {Psi}tc parameter to ensure positivity of the resulting linear system, diagonal dominance and convergence of the two-step scheme. For AMR, a level defines a subdomain for refinement. For diffusive processes such as MGD, the refined level uses Dirichet boundary data at the coarse-fine interface and the data is derived from the coarse level solution. After advancing on the fine level, an additional procedure, the sync-solve (SS), is required in order to enforce conservation. The MGD SS reduces to an elliptic solve on a combined grid for a system of G equations, where G is the number of groups. We adapt the 'partial temperature' scheme for the SS; hence, we reuse the infrastructure developed for scalar equations. Results are presented. We consider a multigroup test problem with a known analytic solution. We demonstrate utility of {Psi}tc by running with increasingly larger timesteps. Lastly, we simulate the sudden release of energy Y inside an Al sphere (r = 15 cm) suspended in air at STP. For Y = 11 kT, we find that gray radiation diffusion and MGD produce similar results. However, if Y = 1 MT, the two packages yield different results. Our large Y simulation contradicts a long-standing theory and demonstrates the inadequacy of gray diffusion.

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PDF-file: 41 pages; size: 0.7 Mbytes

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  • Journal Name: Journal of Computational Physics, vol. 227, no. 3, January 1, 2008, pp. 2154--2186; Journal Volume: 227; Journal Issue: 3

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  • Report No.: UCRL-JRNL-224845
  • Grant Number: W-7405-ENG-48
  • Office of Scientific & Technical Information Report Number: 936954
  • Archival Resource Key: ark:/67531/metadc894060

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  • September 21, 2006

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  • Sept. 27, 2016, 1:39 a.m.

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  • Nov. 29, 2016, 8:37 p.m.

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Shestakov, A I & Offner, S R. A Multigroup diffusion solver using pseudo transient continuation for a radiation-hydrodynamic code with patch-based AMR, article, September 21, 2006; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc894060/: accessed October 23, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.