A Hybrid Finite-Volume, Discontinuous Galerkin Discretization for the Radiative Transport Equation

Heningburg, Vincent E.; Hauck, Cory

doi:10.1137/19m1304520

A Hybrid Finite-Volume, Discontinuous Galerkin Discretization for the Radiative Transport Equation

Journal Article · Wed Jan 06 23:00:00 EST 2021 · Multiscale Modeling & Simulation

DOI:https://doi.org/10.1137/19m1304520· OSTI ID:1846554

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Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Univ. of Tennessee, Knoxville, TN (United States)
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

In this report we propose a hybrid spatial discretization for the radiative transport equation that combines a second-order discontinuous Galerkin (DG) method and a second-order finite-volume (FV) method. The strategy relies on a simple operator splitting that has been used previously to combine different angular discretizations. Unlike standard FV methods with upwind fluxes, the hybrid approach is able to accurately simulate problems in scattering dominated regimes. However, it requires less memory and yields a faster computational time than a uniform DG discretization. In addition, the underlying splitting allows naturally for hybridization in both space and angle. Numerical results are given to demonstrate the efficiency of the hybrid approach in the context of discrete ordinate angular discretizations and Cartesian spatial grids.

View Accepted Manuscript (DOE)

Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC05-00OR22725; AC52-06NA25396

OSTI ID:: 1846554

Journal Information:: Multiscale Modeling & Simulation, Journal Name: Multiscale Modeling & Simulation Journal Issue: 1 Vol. 19; ISSN 1540-3459

Publisher:: SIAMCopyright Statement

Country of Publication:: United States

Language:: English

References (24)

Asymptotic-preserving & well-balanced schemes for radiative transfer and the Rosseland approximation Gosse, Laurent; Toscani, Giuseppe Numerische Mathematik, Vol. 98, Issue 2 https://doi.org/10.1007/s00211-004-0533-x	journal	April 2004
Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes Larsen, Edward W.; Morel, J. E.; Miller, Warren F. Journal of Computational Physics, Vol. 69, Issue 2 https://doi.org/10.1016/0021-9991(87)90170-7	journal	April 1987
Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes II larsen, Edward W.; Morel, J. E. Journal of Computational Physics, Vol. 83, Issue 1 https://doi.org/10.1016/0021-9991(89)90229-5	journal	July 1989
Even-parity finite-element transport methods in the diffusion limit Adams, Marvin L. Progress in Nuclear Energy, Vol. 25, Issue 2-3 https://doi.org/10.1016/0149-1970(91)90007-C	journal	January 1991
An overview of the transport theory of charged particles Zheng-Ming, Luo; Brahme, Anders Radiation Physics and Chemistry, Vol. 41, Issue 4-5 https://doi.org/10.1016/0969-806X(93)90318-O	journal	April 1993
Fast iterative methods for discrete-ordinates particle transport calculations Adams, Marvin L.; Larsen, Edward W. Progress in Nuclear Energy, Vol. 40, Issue 1 https://doi.org/10.1016/S0149-1970(01)00023-3	journal	January 2002
Two-dimensional time dependent Riemann solvers for neutron transport Brunner, Thomas A.; Holloway, James Paul Journal of Computational Physics, Vol. 210, Issue 1 https://doi.org/10.1016/j.jcp.2005.04.011	journal	November 2005
Semi-implicit time integration for thermal radiative transfer McClarren, Ryan G.; Evans, Thomas M.; Lowrie, Robert B. Journal of Computational Physics, Vol. 227, Issue 16 https://doi.org/10.1016/j.jcp.2008.04.029	journal	August 2008
An arbitrary-order, fully implicit, hybrid kinetic solver for linear radiative transport using integral deferred correction Crockatt, Michael M.; Christlieb, Andrew J.; Garrett, C. Kristopher Journal of Computational Physics, Vol. 346 https://doi.org/10.1016/j.jcp.2017.06.017	journal	October 2017
Hybrid methods for radiation transport using diagonally implicit Runge–Kutta and space–time discontinuous Galerkin time integration Crockatt, Michael M.; Christlieb, Andrew J.; Garrett, C. Kristopher Journal of Computational Physics, Vol. 376 https://doi.org/10.1016/j.jcp.2018.09.041	journal	January 2019
Numerical integration on the sphere Atkinson, Kendall The Journal of the Australian Mathematical Society. Series B. Applied Mathematics, Vol. 23, Issue 3 https://doi.org/10.1017/S0334270000000278	journal	January 1982
Two-dimensional hydrodynamic core-collapse supernova simulations with spectral neutrino transport: I. Numerical method and results for a 15 Buras, R.; Rampp, M.; Janka, H. -Th. Astronomy & Astrophysics, Vol. 447, Issue 3 https://doi.org/10.1051/0004-6361:20053783	journal	February 2006
Asymptotic solution of neutron transport problems for small mean free paths Larsen, Edward W.; Keller, Joseph B. Journal of Mathematical Physics, Vol. 15, Issue 1 https://doi.org/10.1063/1.1666510	journal	January 1974
Uniform asymptotic expansions in transport theory with small mean free paths, and the diffusion approximation Habetler, G. J.; Matkowsky, B. J. Journal of Mathematical Physics, Vol. 16, Issue 4 https://doi.org/10.1063/1.522618	journal	April 1975
A Comparison of Moment Closures for Linear Kinetic Transport Equations: The Line Source Benchmark Garrett, C. Kristopher; Hauck, Cory D. Transport Theory and Statistical Physics, Vol. 42, Issue 6-7 https://doi.org/10.1080/00411450.2014.910226	journal	September 2013
An Investigation of Neutrino‐driven Convection and the Core Collapse Supernova Mechanism Using Multigroup Neutrino Transport Mezzacappa, A.; Calder, A. C.; Bruenn, S. W. The Astrophysical Journal, Vol. 495, Issue 2 https://doi.org/10.1086/305338	journal	March 1998
Temporal Regularization of the $P_N$ Equations Hauck, Cory D.; Lowrie, Robert B. Multiscale Modeling & Simulation, Vol. 7, Issue 4 https://doi.org/10.1137/07071024X	journal	January 2009
Diagonally Implicit Runge–Kutta Methods for Stiff O.D.E.’s Alexander, Roger SIAM Journal on Numerical Analysis, Vol. 14, Issue 6 https://doi.org/10.1137/0714068	journal	December 1977
Asymptotic Analysis of Upwind Discontinuous Galerkin Approximation of the Radiative Transport Equation in the Diffusive Limit Guermond, Jean-Luc; Kanschat, Guido SIAM Journal on Numerical Analysis, Vol. 48, Issue 1 https://doi.org/10.1137/090746938	journal	January 2010
Discrete-Ordinate Discontinuous Galerkin Methods for Solving the Radiative Transfer Equation Han, Weimin; Huang, Jianguo; Eichholz, Joseph A. SIAM Journal on Scientific Computing, Vol. 32, Issue 2 https://doi.org/10.1137/090767340	journal	January 2010
A Collision-Based Hybrid Method for Time-Dependent, Linear, Kinetic Transport Equations Hauck, Cory D.; McClarren, Ryan G. Multiscale Modeling & Simulation, Vol. 11, Issue 4 https://doi.org/10.1137/110846610	journal	January 2013
Uniformly Accurate Diffusive Relaxation Schemes for Multiscale Transport Equations Jin, Shi; Pareschi, Lorenzo; Toscani, Giuseppe SIAM Journal on Numerical Analysis, Vol. 38, Issue 3 https://doi.org/10.1137/S0036142998347978	journal	January 2000
A Mixed Variational Framework for the Radiative Transfer Equation Egger, Herbert; Schlottbom, Matthias Mathematical Models and Methods in Applied Sciences, Vol. 22, Issue 03 https://doi.org/10.1142/S021820251150014X	journal	March 2012
Discontinuous Finite Element Transport Solutions in Thick Diffusive Problems Adams, Marvin L. Nuclear Science and Engineering, Vol. 137, Issue 3 https://doi.org/10.13182/NSE00-41	journal	March 2001

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