Convergence of filtered spherical harmonic equations for radiation transport

Frank, Martin; Hauck, Cory D.; Küpper, Kerstin

doi:10.4310/cms.2016.v14.n5.a10

Cited by 28 publications

(33 citation statements)

References 29 publications

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“…A number of authors have investigated the effect of different filter functions [10,13,12,11]. [11] in particular prove global convergence properties of filtered P n expansions, and determined as one may expect, that in smooth problems the order of the filter determines the rate of convergence. For non-smooth problems, it is the underlying smoothness of the transport problem that determines the rate of convergence.…”

Section: Filtered Spherical Harmonicsmentioning

confidence: 99%

“…Over the last several years however, filtered P n (we refer to these as FP n ) approximations have been introduced [9,10,11,12,13,14], which aim to improve conditioning with discontinuities present. This follows the reasoning behind high-order spectral element methods in fields like aeronautics, where the high-order basis functions are filtered near discontinuities while still retaining high-order convergence in smooth regions.…”

Section: Introductionmentioning

confidence: 99%

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Angular adaptivity with spherical harmonics for Boltzmann transport

Dargaville

Buchan

Smedley-Stevenson

et al. 2019

Journal of Computational Physics

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This paper describes an angular adaptivity algorithm for Boltzmann transport applications which uses P n and filtered P n expansions, allowing for different expansion orders across space/energy. Our spatial discretisation is specifically designed to use less memory than competing DG schemes and also gives us direct access to the amount of stabilisation applied at each node. For filtered P n expansions, we then use our adaptive process in combination with this net amount of stabilisation to compute a spatially dependent filter strength that does not depend on a priori spatial information. This applies heavy filtering only where discontinuities are present, allowing the filtered Pn expansion to retain highorder convergence where possible. Regular and goal-based error metrics are shown and both the adapted P n and adapted filtered P n methods show significant reductions in DOFs and runtime. The adapted filtered P n with our spatially dependent filter shows close to fixed iteration counts and up to high-order is even competitive with P 0 discretisations in problems with heavy advection.

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Section: Filtered Spherical Harmonicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Angular adaptivity with spherical harmonics for Boltzmann transport

Dargaville

Buchan

Smedley-Stevenson

et al. 2019

Journal of Computational Physics

View full text Add to dashboard Cite

show abstract

“…Results confirming Eq. 38 are similarly obtained for the exponential filters of an arbitrary order (which are introduced in [32] Table 6:…”

Section: Comparison To Error Estimatesmentioning

confidence: 94%

Implicit filtered P for high-energy density thermal radiation transport using discontinuous Galerkin finite elements

Labouré

McClarren

Hauck

2016

Journal of Computational Physics

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In this work, we provide a fully-implicit implementation of the time-dependent, filtered spherical harmonics (FP N ) equations for non-linear, thermal radiative transfer. We investigate local filtering strategies and analyze the effect of the filter on the conditioning of the system, showing in particular that the filter improves the convergence properties of the iterative solver. We also investigate numerically the rigorous error estimates derived in the linear setting, to determine whether they hold also for the non-linear case. Finally, we simulate a standard test problem on an unstructured mesh and make comparisons with implicit Monte-Carlo (IMC) calculations.

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“…In the exponential filter, α ∈ N and c = log( M ) where M is the machine accuracy. The Lanczos and Spherical Spline filters are used in [59] while the exponential filter is considered in [60] The main difference between the filters is their order. Roughly speaking, the higher the order, the less the filter will give smooth solutions (think of an unfiltered calculation as a filter of order ∞).…”

Section: )mentioning

confidence: 99%

Rattlesnake Theory Manual

Wang

Labouré

2018

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Rattlesnake is built on the MOOSE framework. Rattlesnake manages meshes with libMesh [25] and solves the system equation with PETSc [26] through MOOSE. Support of unstructured meshes, parallelization with domain decomposition, various time integration schemes, most of nonlinear solvers features, multiphysics coupling are all inherited from the framework. Rattlesnake is responsible for setting up the discretization of RTE with interfaces provided by MOOSE. Because Rattlesnake is built on a general framework, it can perform calculations in 1D, 2D and 3D unstructured meshes via MPI (message passing interface) [27] and multi-threading. The weak forms can be directly translated into code under the MOOSE framework, which results in codes easy to maintain and extend. Multiple developers can co-work seamlessly on Rattlesnake. This development pattern allows splitting the work into the physics-related items residing in Rattlesnake, and physics-irrelevant items residing in the framework. The benefit is twofold: Rattlesnake can push the development on the framework side, which can benefit all the other MOOSE-based applications and any improvements in MOOSE can improve Rattlesnake. For example, the common software development procedure is managed by MOOSE, e.g. the version control, regression tests, on-line documentation. In addition, coupling Rattlesnake with other MOOSE-based applications dealing with other physics is straightforward because these applications are based on the same framework. As an example, the reactor physics application MAMMOTH [2, 28] leverages components spread over Rattlesnake, MOOSE and its modules, Bison [29, 30, 31], and Relap-7 [32]. In summary, being built on MOOSE makes Rattlesnake powerful and unique. There indeed are constraints imposed by the framework, but this is not insurmountable and outweighted by all the advantages provided by this development pattern. In Section 2, we first state the RTE for various particles. Currently, we only consider two particles: neutron and thermal radiation but Rattlesnake can be extended easily to other types. Particles mostly share the same time derivative,

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Convergence of filtered spherical harmonic equations for radiation transport

Cited by 28 publications

References 29 publications

Angular adaptivity with spherical harmonics for Boltzmann transport

Angular adaptivity with spherical harmonics for Boltzmann transport

Implicit filtered P for high-energy density thermal radiation transport using discontinuous Galerkin finite elements

Rattlesnake Theory Manual

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