Methods for coupling radiation, ion, and electron energies in grey Implicit Monte Carlo

Evans, Thomas M.; Densmore, Jeffery D.

doi:10.1016/j.jcp.2007.02.020

Cited by 13 publications

(7 citation statements)

References 9 publications

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“…One of the benefits of these self-similar solutions is that they can be used to verify numerical codes built to solve high-energy density radiative transfer and radiation hydrodynamics. Despite the fact that the problem formulations are nearly singular in the neighbourhood of t = 0 for the time-dependent model and x = 0 for the space-dependent model, we are able to reproduce the solution with a finite volume solver for the radiation diffusion system [28–30] using the 3-T model of Evans & Densmore [3].…”

Section: Resultsmentioning

confidence: 99%

“…If the temperatures are not too different, then γ is proportional to Te−3/2 and the electron number density [27]. It is also common in many analyses to choose a constant value for γ when producing results [3,6].…”

Section: Model Equations For Coupling Radiation Electron and Ion Energiesmentioning

confidence: 99%

“…the Sedov–Taylor blast wave [20–22]) are used for code verification. A survey of the current literature indicates that there is a need for benchmarks for problems with radiation, electron and ion coupling: the extant solutions that exist are for infinite media [3,23] or shock waves without radiation effects [24].…”

Section: Introductionmentioning

confidence: 99%

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Self-similar solutions for high-energy density radiative transfer with separate ion and electron temperatures

Bennett

McClarren

2021

Proc. R. Soc. A.

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We consider a non-equilibrium plasma radiatively heated by an external source in the high-energy density regime. It is shown that self-similar solutions resembling the classic Marshak wave exist for the ion and electron temperatures, if the electron–ion coupling coefficient scales inversely proportional to either the time from when the heating begins or to the square of the distance from the surface of the plasma. We discuss how such a coupling coefficient may arise, and demonstrate that these solutions are also useful for verifying simulation codes that treat radiation–electron–ion coupling in high-energy density plasmas.

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Section: Resultsmentioning

confidence: 99%

Section: Model Equations For Coupling Radiation Electron and Ion Energiesmentioning

confidence: 99%

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Self-similar solutions for high-energy density radiative transfer with separate ion and electron temperatures

Bennett

McClarren

2021

Proc. R. Soc. A.

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“…We also note that the system of equations solved in ENRICO also has similarities to frameworks that solve coupled radiation-hydrodynamics problems. 27 However there are substantial differences: The radiationhydrodynamics equations are highly nonlinear and time dependent 28,29 and generally require solutions on conformal grids. Furthermore, because of the tight, two-way coupling between the hydrodynamic and radiation equations, highorder time solutions require full convergence of the nonlinearities in each time step.…”

Section: Introductionmentioning

confidence: 99%

A Code-Agnostic Driver Application for Coupled Neutronics and Thermal-Hydraulic Simulations

Romano

Hamilton

Rahaman

et al. 2020

Nuclear Science and Engineering

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While the literature has numerous examples of Monte Carlo (MC) and computational fluid dynamics (CFD) coupling, most are hardwired codes intended primarily for research rather than as stand-alone, generalpurpose applications. In this work, we describe an open source application, the Exascale Nuclear Reactor Investigative COde (ENRICO), which enables coupled neutronic and thermal-hydraulic simulations between multiple codes that can be chosen at run time (as opposed to a coupling between two specific codes). The application has been designed such that the control flow logic, domain mapping, nonlinear fixed-point iteration, solution transfers, and convergence checks are all agnostic to the underlying physics solvers used. Special emphasis has also been placed on enabling efficient execution on distributed-memory computing environments. The transfer of solution fields between solvers is performed in memory rather than through filesystem input/output. Additionally, solvers can be configured to run on overlapping or disjoint sets of processes. To date, coupling with the OpenMC and Shift MC codes, the Nek5000 CFD code, and a simplified heat diffusion and subchannel solver has been implemented in ENRICO. We present results for coupled simulations of a single light water reactor fuel assembly based on the NuScale reactor using various combinations of the physics solvers. For this problem, the coupled simulations are shown to converge in about four Picard iterations. A comparison of the heat source and temperature distributions computed by ENRICO using OpenMC coupled with Nek5000 and Shift coupled with Nek5000 illustrates remarkable agreement between the codes.

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“…Many of these physics can be fitted to the fundamental IMC methodology, but they would muddy its presentation. Finally, we do not formally include physical scattering in our derivation; reincorporating Thomson scattering is straightforward, and there are also techniques to implement Compton scattering (Carter and Forest, 1973;Castor, 2004;Densmore, Warsa, and Lowrie, 2010;Densmore et al, 2009;Densmore, Warsam and Morel, 2007;Dolence et al, 2009;Evans and Densmore, 2007;Fleck, 1971;Hungerford, Densmore, and Buksas, 2005;Pomraning, 1973). The equations that model this system are 1 c…”

Section: Introductionmentioning

confidence: 99%

Four Decades of Implicit Monte Carlo

Wollaber

2016

Journal of Computational and Theoretical Transport

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In 1971, Fleck and Cummings derived a system of equations to enable robust Monte Carlo simulations of time-dependent, thermal radiative transfer problems. Denoted the "Implicit Monte Carlo" (IMC) equations, their solution remains the de facto standard of high-fidelity radiative transfer simulations. Over the course of 44 years, their numerical properties have become better understood, and accuracy enhancements, novel acceleration methods, and variance reduction techniques have been suggested. In this review, we rederive the IMC equations-explicitly highlighting assumptions as they are made-and outfit the equations with a Monte Carlo interpretation. We put the IMC equations in context with other approximate forms of the radiative transfer equations and present a new demonstration of their equivalence to another well-used linearization solved with deterministic transport methods for frequency-independent problems. We discuss physical and numerical limitations of the IMC equations for asymptotically small time steps, stability characteristics and the potential of maximum principle violations for large time steps, and solution behaviors in an asymptotically thick diffusive limit. We provide a new stability analysis for opacities with general monomial dependence on temperature. We consider spatial accuracy limitations of the IMC equations and discussion acceleration and variance reduction techniques.

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Methods for coupling radiation, ion, and electron energies in grey Implicit Monte Carlo

Cited by 13 publications

References 9 publications

Self-similar solutions for high-energy density radiative transfer with separate ion and electron temperatures

Self-similar solutions for high-energy density radiative transfer with separate ion and electron temperatures

A Code-Agnostic Driver Application for Coupled Neutronics and Thermal-Hydraulic Simulations

Four Decades of Implicit Monte Carlo

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