An exact solution for the linearized multifrequency radiation diffusion equation

Shestakov, A. I.; Bolstad, J.H.

doi:10.1016/j.jqsrt.2004.05.052

Cited by 10 publications

(12 citation statements)

References 3 publications

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“…In Section 5.1, we present a test problem with a known analytic solution. We compare numerical results with tabular data, previously published by Shestakov and Bolstad [21]. Using Richardson extrapolation, we show that our Wtc scheme, i.e., what we apply on a level, is second (first) order correct in space (time).…”

Section: Simulationsmentioning

confidence: 74%

“…Due to the nonlinearity of the equations, there are no test problems with analytic solutions. Thus, to validate and verify our algorithm, we consider the linearized multigroup equations developed by Shestakov and Bolstad (S&B) [21] and compare with tabular data.…”

Section: Linear Mgd Test Problemmentioning

confidence: 99%

“…A misprint in[21] erroneously has m 1 = 10 À4 10. For each point, f k is the arithmetic average of the two adjoining cell-centered values 11.…”

mentioning

confidence: 99%

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

Shestakov

Offner

2008

Journal of Computational Physics

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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 (Wtc). We analyze the magnitude of the Wtc 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 Dirichlet 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 Wtc 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. Published by Elsevier Inc.

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Section: Simulationsmentioning

confidence: 74%

Section: Linear Mgd Test Problemmentioning

confidence: 99%

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

Shestakov

Offner

2008

Journal of Computational Physics

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“…Its spectrum is of interest only insomuch as it affects the calculation of µ and λ; it is not calculated by the equations described herein. The spectrum may be the result of a simultaneous multifrequency-gray calculation (as described by Winslow and others [53,61,62,63]) of which these equations form the gray pass. Or it may be assumed to be that of a Planckian at temperature θ, or even at temperature T R .…”

Section: Energy Equations: Generalmentioning

confidence: 99%

The RAGE radiation-hydrodynamic code

et al. 2008

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We describe RAGE, the "Radiation Adaptive Grid Eulerian" radiation-hydrodynamics code, including its data structures, its parallelization strategy and performance, its hydrodynamic algorithm(s), its (gray) radiation diffusion algorithm, and some of the considerable amount of verification and validation efforts. The hydrodynamics is a basic Godunov solver, to which we have made significant improvements to increase the advection algorithm's robustness and to converge stiffnesses in the equation of state. Similarly, the radiation transport is a basic gray diffusion, but our treatment of the radiation-material coupling, wherein we converge nonlinearities in a novel manner to allow larger timesteps and more robust behavior, can be applied to any multi-group transport algorithm.

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“…Shestakov & Bolstad Problem* This problem, discussed in [She05], presents exact solutions for a linearization of a system modeling the multifrequency radiation diffusion and matter energy balance equations. Based on an approach similar to that in [Su97], this test problem incorporates more realistic assumptions regarding the opacity and the specific heat.…”

Section: Transport Processes 3a Lowrie-rauenzahn Equilibrium-diffusimentioning

confidence: 99%

Enhanced verification test suite for physics simulation codes

Kamm¹,

Brock²,

Brandon³

et al. 2008

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Executive SummaryThis document discusses problems with which to augment, in quantity and in quality, the existing tri-laboratory suite of verification problems used by Los Alamos National Laboratory (LANL), Lawrence Livermore National Laboratory (LLNL), and Sandia National Laboratories (SNL). The purpose of verification analysis is demonstrate whether the numerical results of the discretization algorithms in physics and engineering simulation codes provide correct solutions of the corresponding continuum equations. The key points of this document are:• Verification deals with mathematical correctness of the numerical algorithms in a code, while validation deals with physical correctness of a simulation in a regime of interest. This document is about verification.• The current seven-problem Tri-Laboratory Verification Test Suite, which has been used for approximately five years at the DOE WP laboratories, is limited.• Both the methodology for and technology used in verification analysis have evolved and been improved since the original test suite was proposed.• The proposed test problems are in three basic areas:1. Hydrodynamics 2. Transport processes 3. Dynamic strength-of-materials• For several of the proposed problems we provide a "strong sense verification benchmark," consisting of (i) a clear mathematical statement of the problem with sufficient information to run a computer simulation, (ii) an explanation of how the code result and benchmark solution are to be evaluated, and (iii) a description of the acceptance criterion for simulation code results.

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An exact solution for the linearized multifrequency radiation diffusion equation

Cited by 10 publications

References 3 publications

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

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

The RAGE radiation-hydrodynamic code

Enhanced verification test suite for physics simulation codes

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