Robust and accurate filtered spherical harmonics expansions for radiative transfer

McClarren, Ryan G.; Hauck, Cory D.

doi:10.1016/j.jcp.2010.03.043

Cited by 112 publications

(89 citation statements)

References 33 publications

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“…In multi-dimensional settings, it is known that analytical solutions to the P 1 model (for which v = 1/3) and for spherical harmonic closures in general can yield values of E that are negative [8,40,42,43,47,48]. Moreover, in steady-state cases, the P 1 model predicts that F = c(3r t ) À1 @ x E, which near discontinuities is unbounded and thus inconsistent with (4).…”

Section: Introductionmentioning

confidence: 99%

A realizability-preserving discontinuous Galerkin method for the M1 model of radiative transfer

Olbrant

Hauck

Frank

2012

Journal of Computational Physics

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Section: Introductionmentioning

confidence: 99%

A realizability-preserving discontinuous Galerkin method for the M1 model of radiative transfer

Olbrant

Hauck

Frank

2012

Journal of Computational Physics

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“…In order to further reduce the overall memory footprint, the filtered spherical harmonics approach to momentum space angular discretization [29,41] may be an attractive option for core-collapse supernova neutrino transport simulations. However, proper inclusion of all the relevant physics discussed above remains a forefront research topic in computational physics.…”

Section: Discussionmentioning

confidence: 99%

Bound-preserving discontinuous Galerkin methods for conservative phase space advection in curvilinear coordinates

Endeve

Hauck

Xing

et al. 2015

Journal of Computational Physics

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We extend the positivity-preserving method of Zhang and Shu [49] to simulate the advection of neutral particles in phase space using curvilinear coordinates. The ability to utilize these coordinates is important for non-equilibrium transport problems in general relativity and also in science and engineering applications with specific geometries. The method achieves high-order accuracy using Discontinuous Galerkin (DG) discretization of phase space and strong stability-preserving, Runge-Kutta (SSP-RK) time integration. Special care is taken to ensure that the method preserves strict bounds for the phase space distribution function f ; i.e., f ∈ [0, 1]. The combination of suitable CFL conditions and the use of the high-order limiter proposed in [49] is sufficient to ensure positivity of the distribution function. However, to ensure that the distribution function satisfies the upper bound, the discretization must, in addition, preserve the divergence-free property of the phase space flow. Proofs that highlight the necessary conditions are presented for general curvilinear coordinates, and the details of these conditions are worked out for some commonly used coordinate systems (i.e., spherical polar spatial coordinates in spherical symmetry and cylindrical spatial coordinates in axial symmetry, both with spherical momentum coordinates). Results from numerical experiments -including one example in spherical symmetry adopting the Schwarzschild metric -demonstrate that the method achieves high-order accuracy and that the distribution function satisfies the maximum principle.

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“…The first problem we solve involves a checkerboard of highly absorbing material embedded in a scattering material. This problem, originally posed in [52,53], has become a common test problem of angular discretizations of the transport equation (see, for example, [54,55,56]). The layout and Monte Carlo solution [53] for the problem are shown in Figure 5.…”

Section: Implementation Detailsmentioning

confidence: 99%

A Collision-Based Hybrid Method for Time-Dependent, Linear, Kinetic Transport Equations

Hauck¹,

McClarren²

2013

Multiscale Model. Simul.

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We present a hybrid method for simulating kinetic equations with multiscale phenomena in the context of linear transport. The method consists of (i) partitioning the kinetic equation into collisional and noncollisional components, (ii) applying a different numerical method to each component, and (iii) repartitioning the kinetic distribution after each time step in the algorithm. Preliminary results show that, for a wide range of test problems, the combination of a low-fidelity method for the collisional component and a high-fidelity method for the noncollisional component provides a level of accuracy that is comparable to a uniform high-fidelity treatment of the entire system.

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Robust and accurate filtered spherical harmonics expansions for radiative transfer

Cited by 112 publications

References 33 publications

A realizability-preserving discontinuous Galerkin method for the M1 model of radiative transfer

A realizability-preserving discontinuous Galerkin method for the M1 model of radiative transfer

Bound-preserving discontinuous Galerkin methods for conservative phase space advection in curvilinear coordinates

A Collision-Based Hybrid Method for Time-Dependent, Linear, Kinetic Transport Equations

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