A Multigroup diffusion Solver Using Pseudo Transient Continuation for a RadiaitonHydrodynamic Code with PatchBased AMR
Abstract
We present a scheme to solve the nonlinear multigroup radiation diffusion (MGD) equations. The method is incorporated into a massively parallel, multidimensional, Eulerian radiationhydrodynamic code with adaptive mesh refinement (AMR). The patchbased AMR algorithm refines in both space and time creating a hierarchy of levels, coarsest to finest. The physics modules are timeadvanced using operator splitting. On each level, separate 'levelsolve' packages advance the modules. Our multigroup levelsolve adapts an implicit procedure which leads to a twostep iterative scheme that alternates between elliptic solves for each group with intracell 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 twostep 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 coarsefine interface and the data is derived from the coarse level solution. After advancing on the fine level, an additional procedure, the syncsolve (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 themore »
 Authors:
 Publication Date:
 Research Org.:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 940501
 Report Number(s):
 UCRLJRNL228646
Journal ID: ISSN 00219991; JCTPAH; TRN: US200824%%64
 DOE Contract Number:
 W7405ENG48
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Computational Physics, vol. 227, no. 3, January 1, 2008, pp. 21542186; Journal Volume: 227; Journal Issue: 3
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUMM MECHANICS, GENERAL PHYSICS; AIR; ALGORITHMS; CONVERGENCE; DIFFUSION; PHYSICS; RADIATIONS; SCALARS; SIMULATION; TRANSIENTS
Citation Formats
Shestakov, A I, and Offner, S R. A Multigroup diffusion Solver Using Pseudo Transient Continuation for a RadiaitonHydrodynamic Code with PatchBased AMR. United States: N. p., 2007.
Web.
Shestakov, A I, & Offner, S R. A Multigroup diffusion Solver Using Pseudo Transient Continuation for a RadiaitonHydrodynamic Code with PatchBased AMR. United States.
Shestakov, A I, and Offner, S R. Fri .
"A Multigroup diffusion Solver Using Pseudo Transient Continuation for a RadiaitonHydrodynamic Code with PatchBased AMR". United States.
doi:. https://www.osti.gov/servlets/purl/940501.
@article{osti_940501,
title = {A Multigroup diffusion Solver Using Pseudo Transient Continuation for a RadiaitonHydrodynamic Code with PatchBased AMR},
author = {Shestakov, A I and Offner, S R},
abstractNote = {We present a scheme to solve the nonlinear multigroup radiation diffusion (MGD) equations. The method is incorporated into a massively parallel, multidimensional, Eulerian radiationhydrodynamic code with adaptive mesh refinement (AMR). The patchbased AMR algorithm refines in both space and time creating a hierarchy of levels, coarsest to finest. The physics modules are timeadvanced using operator splitting. On each level, separate 'levelsolve' packages advance the modules. Our multigroup levelsolve adapts an implicit procedure which leads to a twostep iterative scheme that alternates between elliptic solves for each group with intracell 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 twostep 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 coarsefine interface and the data is derived from the coarse level solution. After advancing on the fine level, an additional procedure, the syncsolve (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 longstanding theory and demonstrates the inadequacy of gray diffusion.},
doi = {},
journal = {Journal of Computational Physics, vol. 227, no. 3, January 1, 2008, pp. 21542186},
number = 3,
volume = 227,
place = {United States},
year = {Fri Mar 02 00:00:00 EST 2007},
month = {Fri Mar 02 00:00:00 EST 2007}
}

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

A multigroup diffusion solver using pseudo transient continuation for a radiationhydrodynamic code with patchbased AMR
We present a scheme to solve the nonlinear multigroup radiation diffusion (MGD) equations. The method is incorporated into a massively parallel, multidimensional, Eulerian radiationhydrodynamic code with Adaptive Mesh Refinement (AMR). The patchbased AMR algorithm refines in both space and time creating a hierarchy of levels, coarsest to finest. The physics modules are timeadvanced using operator splitting. On each level, separate 'levelsolve' packages advance the modules. Our multigroup levelsolve adapts an implicit procedure which leads to a twostep iterative scheme that alternates between elliptic solves for each group with intracell group coupling. For robustness, we introduce pseudo transient continuation ({psi}tc). Wemore » 
An AMR capable finite element diffusion solver for ALE hydrocodes [An AMR capable diffusion solver for ALEAMR]
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Solution of the nonlinear multifrequency radiation diffusion equations using pseudo transient continuation
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