StaRMAP

StaRMAP—A second order staggered grid method for spherical harmonics moment equations of radiative transfer. We present a simple method to solve spherical harmonics moment systems, such as the the time-dependent PN and SPN equations, of radiative transfer. The method, which works for arbitrary moment order N, makes use of the specific coupling between the moments in the PN equations. This coupling naturally induces staggered grids in space and time, which in turn give rise to a canonical, second-order accurate finite difference scheme. While the scheme does not possess TVD or realizability limiters, its simplicity allows for a very efficient implementation in Matlab. We present several test cases, some of which demonstrate that the code solves problems with ten million degrees of freedom in space, angle, and time within a few seconds. The code for the numerical scheme, called StaRMAP (Staggered grid Radiation Moment Approximation), along with files for all presented test cases, can be downloaded so that all results can be reproduced by the reader.


References in zbMATH (referenced in 17 articles , 1 standard article )

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  1. Anguill, Pierre; Cargo, Patricia; Énaux, Cedric; Hoch, Philippe; Labourasse, Emmanuel; Samba, Gerald: An asymptotic preserving method for the linear transport equation on general meshes (2022)
  2. Hermeline, Francois: Discrete duality finite volume discretization of the thermal-(P_N) radiative transfer equations on general meshes (2022)
  3. Schneider, Florian; Leibner, Tobias: First-order continuous- and discontinuous-Galerkin moment models for a linear kinetic equation: realizability-preserving splitting scheme and numerical analysis (2022)
  4. Leibner, Tobias; Ohlberger, Mario: A new entropy-variable-based discretization method for minimum entropy moment approximations of linear kinetic equations (2021)
  5. Sarna, Neeraj; Kapadia, Harshit; Torrilhon, Manuel: Simultaneous-approximation-term based boundary discretization for moment equations of rarefied gas dynamics (2020)
  6. Schneider, Florian; Leibner, Tobias: First-order continuous- and discontinuous-Galerkin moment models for a linear kinetic equation: model derivation and realizability theory (2020)
  7. Hauck, Cory; Heningburg, Vincent: Filtered discrete ordinates equations for radiative transport (2019)
  8. Laiu, M. Paul; Frank, Martin; Hauck, Cory D.: A positive asymptotic-preserving scheme for linear kinetic transport equations (2019)
  9. Pu, Can; McClarren, Ryan G.: Mathematical and numerical validation of the simplified spherical harmonics approach for time-dependent anisotropic-scattering transport problems in homogeneous media (2017)
  10. Egger, Herbert; Schlottbom, Matthias: A class of Galerkin schemes for time-dependent radiative transfer (2016)
  11. Frank, Martin; Hauck, Cory; Küpper, Kerstin: Convergence of filtered spherical harmonic equations for radiation transport (2016)
  12. Hermeline, F.: A discretization of the multigroup (P_N) radiative transfer equation on general meshes (2016)
  13. Küpper, Kerstin; Frank, Martin; Jin, Shi: An asymptotic preserving two-dimensional staggered grid method for multiscale transport equations (2016)
  14. Schneider, Florian: Kershaw closures for linear transport equations in slab geometry. II: High-order realizability-preserving discontinuous-Galerkin schemes (2016)
  15. Schneider, Florian: Kershaw closures for linear transport equations in slab geometry. I: Model derivation (2016)
  16. Seibold, Benjamin; Frank, Martin: StaRMAP -- a second order staggered grid method for spherical harmonics moment equations of radiative transfer (2014)
  17. Olbrant, E.; Larsen, E. W.; Frank, M.; Seibold, B.: Asymptotic derivation and numerical investigation of time-dependent simplified image equations (2013)