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Convergence of filtered spherical harmonic equations for radiation transport

Journal Article · · Communications in Mathematical Sciences
 [1];  [2];  [1]
  1. RWTH Aachen Univ. (Germany)
  2. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Univ. of Tennessee, Knoxville, TN (United States)

In this work, we analyze the global convergence properties of the filtered spherical harmonic (FPN) equations for radiation transport. The well-known spherical harmonic (PN) equations are a spectral method (in angle) for the radiation transport equation and are known to suffer from Gibbs phenomena around discontinuities. The filtered equations include additional terms to address this issue that are derived via a spectral filtering procedure. We show explicitly how the global $L^2$ convergence rate (in space and angle) of the spectral method to the solution of the transport equation depends on the smoothness of the solution (in angle only) and on the order of the filter. The results are confirmed by numerical experiments. Numerical tests have been implemented in MATLAB and are available online.

Research Organization:
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
Sponsoring Organization:
USDOE; National Science Foundation (NSF)
Grant/Contract Number:
AC05-00OR22725
OSTI ID:
1845815
Journal Information:
Communications in Mathematical Sciences, Journal Name: Communications in Mathematical Sciences Journal Issue: 5 Vol. 14; ISSN 1539-6746
Publisher:
International PressCopyright Statement
Country of Publication:
United States
Language:
English

Cited By (2)

Positivity Limiters for Filtered Spectral Approximations of Linear Kinetic Transport Equations journal August 2018
Filtered Discrete Ordinates Equations for Radiative Transport journal May 2019

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