Physics-Based Preconditioning and the Newton–Krylov Method for Non-equilibrium Radiation Diffusion

Mousseau, Vincent; Knoll, D. A.; Rider, William J.

doi:10.1006/jcph.2000.6488

Cited by 113 publications

(85 citation statements)

References 23 publications

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“…6.6. Note that the results given by Mousseau in [113] for the same test problem do not match the solutions shown here. The wave propagation speed of the energy source due to the left boundary condition is resolved differently in Fig.…”

Section: Resultscontrasting

confidence: 63%

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Neutronic/Thermalhydraulic Coupling Technigues for Sodium Cooled Fast Reactor Simulations

Ragusa¹,

Siegel²,

Ruggieri³

2010

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Executive SummaryThe objective of this project was to test new coupling algorithms and enable efficient and scalable multi-physics simulations of advanced nuclear reactors, with considerations regarding the implementation of such algorithms in massively parallel environments. Numerical tests were carried out to verify the proposed approach and the examples included some reactor transients. The project was directly related to the Sodium Fast Reactor program element of the Generation IV Nuclear Energy Systems Initiative and the Advanced Fuel cycle Initiative, and, supported the requirement of high-fidelity simulation as a mean of achieving the goals of the presidential Global Nuclear Energy Partnership (GNEP) vision.For decades, the modeling of nuclear cores has been divided into several distinct domains of physics: neutronics, hydraulics, heat transfer, … Yet, these physical models describe physical processes that are tightly intertwined and rely heavily on the solution field of one another. In the last decade or so, various existing mono-disciplinary codes have been coupled together in a naive "black-box" fashion, where the output of one code serves as the input of another code, producing nonlinearly inconsistent multiphysics solutions. Such schemes, which are still the main coupling paradigm today for solving nonlinear nuclear reactor physics equations, are based on a linearization of the coupling terms that is never resolved and that can lead to a loss of accuracy and stability in the solution procedure. In order to address the inconsistencies of traditional coupling strategies, a 3-D test-bed code based on reduced physical models has been developed. It includes several physic components, namely, multigroup neutron diffusion, monophasic fluid conservation laws (mass, momentum, energy), nonlinear heat conduction. This test-bed code was used to demonstrate the loss of accuracy order due to traditional operator-split techniques used in conventional coupling schemes; to implement Jacobian-free full resolution coupling schemes; to develop adaptive preconditioning techniques; and to investigate high-order time discretizations and adaptive time stepping strategies. The test-bed code employs state-of-the-art algorithms and libraries, namely the Jacobian0free Newton-Krylov technique to solve consistently fully implicit tightly coupled simulations and the ANL's PETSc library of linear and nonlinear solvers for scalability. We have demonstrated that the multiphysics solution procedure yields highly accurate solutions in space and time and is amenable for space/time adaptivity. This portion of the work is discussed in Part A of this report.It is widely agreed that high fidelity simulations is an utmost important tool for the conception, design and validation of complex physical systems such as nuclear reactors. Examples of such thrust can be seen in the ASCI program and the SciDAC program. GNEP strongly advocates the development of the next-generation simulation software with a far wider range of applicability than conven...

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Section: Resultscontrasting

confidence: 63%

“…The definitions for these material properties [113] are (6.25) with z being the material atomic number and k is a constant.…”

Section: Closing Remarksmentioning

confidence: 99%

Neutronic/Thermalhydraulic Coupling Technigues for Sodium Cooled Fast Reactor Simulations

Ragusa¹,

Siegel²,

Ruggieri³

2010

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“…Diffusion [15,12,14,11,9,43,25,38,6,5,31,35,44,46,27,37,1,42,41,28] 3. Spherical Harmonics (P N ) [7,10,40,13] 4.…”

Section: The Approximationsmentioning

confidence: 99%

Forms of Approximate Radiation Transport

Brunner

2002

126

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Photon radiation transport is described by the Boltzmann equation. Because this equation is difficult to solve, many different approximate forms have been implemented in computer codes. Several of the most common approximations are reviewed, and test problems illustrate the characteristics of each of the approximations. This document is designed as a tutorial so that code users can make an educated choice about which form of approximate radiation transport to use for their particular simulation.4

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“…Several types of preconditioners have been tested to gain insight into the physics-based preconditioning techniques; these techniques that have been proven to be quite efficient (see [5,6]). Few preconditioners that are trivial to compute and solve, such as a Point Jacobi or a Gauss Seidel preconditioner, can be quite devastating in terms of performance for certain kinds of problems.…”

Section: Preconditioning Techniquesmentioning

confidence: 99%

Coupling Schemes for Multiphysics Reactor Simulation

Mahadeven¹,

Ragusa²

2007

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Physics-Based Preconditioning and the Newton–Krylov Method for Non-equilibrium Radiation Diffusion

Cited by 113 publications

References 23 publications

Neutronic/Thermalhydraulic Coupling Technigues for Sodium Cooled Fast Reactor Simulations

Neutronic/Thermalhydraulic Coupling Technigues for Sodium Cooled Fast Reactor Simulations

Forms of Approximate Radiation Transport

Coupling Schemes for Multiphysics Reactor Simulation

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