Parallel solvers for the transient multigroup neutron diffusion equations

R. Scheichl

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4 Citations (SciVal)


For the safety and the control of a nuclear power plant it is necessary to simulate the constituent processes on a computer system. The three-dimensional multigroup neutron diffusion equations are commonly used to describe the nuclear fission in the reactor core. They form a complicated system of coupled parabolic partial differential equations (PDEs) whose solution can involve very intensive computing. In this paper this system of PDEs is discretized using a special cell-centred mixed finite volume method (NEM-MO) in space, and a method that combines Crank-Nicholson and the BDF(2)-method in time. The linear equation systems which arise are solved with multi-grid as well as with preconditioned BiCGStab. The kernel of both solution methods is an effective Block-SOR method that makes use of the particular structure of the linear equation systems. The parallelization strategy is based on a grid partitioning that distributes the data and the work homogeneously on the processors. Finally, the program was tested for three typical reactor simulation problems on grids with differing coarseness. The speedup achieved by parallelizing multi-grid and preconditioned Bi-CGStab was outstanding for all examples; even superlinear in some cases. Moreover, the parallel execution times were better than the parallel execution times of other established reactor simulation codes.

Original languageEnglish
Pages (from-to)1751-1771
Number of pages21
JournalInternational Journal for Numerical Methods in Engineering
Issue number10
Publication statusPublished - 10 Apr 2000

Bibliographical note

Copyright 2017 Elsevier B.V., All rights reserved.


  • Mixed finite volume discretisation
  • Non-symmetric matrices
  • Parallel Bi-CGStab
  • Parallel multi-grid
  • Transient multigroup neutron diffusion equations

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics


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