Asymptotic derivation and numerical investigation of time-dependent simplified P N equations

  • Authors:

  • E. Olbrant;E. W. Larsen;M. Frank;B. Seibold

  • Affiliations:

  • RWTH Aachen University, Department of Mathematics & Center for Computational Engineering Science, Schinkelstrasse 2, D-52062 Aachen, Germany;University of Michigan, Department of Nuclear Engineering and Radiological Sciences, Ann Arbor, MI 48109-2104, USA;RWTH Aachen University, Department of Mathematics & Center for Computational Engineering Science, Schinkelstrasse 2, D-52062 Aachen, Germany;Department of Mathematics, Temple University, 1805 North Broad Street, Philadelphia, PA 19122, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2013

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Abstract

The steady-state simplified P"N (SP"N) approximations to the linear Boltzmann equation have been proven to be asymptotically higher-order corrections to the diffusion equation in certain physical systems. In this paper, we present an asymptotic analysis for the time-dependent simplified P"N equations up to N=3. Additionally, SP"N equations of arbitrary order are derived in an ad hoc way. The resulting SP"N equations are hyperbolic and differ from those investigated in a previous work by some of the authors. In two space dimensions, numerical calculations for the P"N and SP"N equations are performed. We simulate neutron distributions of a moving rod and present results for a benchmark problem, known as the checkerboard problem. The SP"N equations are demonstrated to yield significantly more accurate results than diffusion approximations. In addition, for sufficiently low values of N, they are shown to be more efficient than P"N models of comparable cost.