Error analysis of the nodal expansion method for solving the neutron diffusion equation

Journal Article · Sat Mar 01 04:00:00 EST 1997 · Nuclear Science and Engineering

OSTI ID:449574

Penland, R C; Turinsky, P J ^[1]; Azmy, Y Y ^[2]

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1. North Carolina State Univ., Raleigh, NC (United States)
2. Oak Ridge National Lab., TN (United States)

Modern nodal methods allow the solution of the few-group neutron diffusion equation in multidimensions to be computed efficiently with high fidelity. This has made possible the routine utilization of three-dimensional analysis for the eigenvalue calculations associated with reload core analysis of light water reactors. Here, an error analysis is presented of the quartic polynomial nodal expansion method for solving the one-dimensional, neutron diffusion equation that originates from employing the transverse integration technique. Error bound expressions are determined for the L{sub {infinity}} error norms associated with the nodal surface flux and various moments of the nodal flux. Employing several test problems, these global error bounds were found to be conservative, but not excessively, in bounding the true errors. Utilizing a functional form of the local error estimate for the node average flux, it is shown that a mesh-doubling technique can be effectively utilized to estimate the required cell size for uniform mesh refinement to achieve a specified global error fidelity. When employed in conjunction with a multigrid acceleration technique, this provides the foundations upon which to develop an adaptive spatial mesh algorithm.

• OSTI ID: 449574
• Journal Information: Nuclear Science and Engineering, Journal Name: Nuclear Science and Engineering Journal Issue: 3 Vol. 125; ISSN NSENAO; ISSN 0029-5639
• Country of Publication: United States
• Language: English

Related Subjects

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS
ERRORS
NEUTRON DIFFUSION EQUATION
NODAL EXPANSION METHOD
REACTOR KINETICS
WATER COOLED REACTORS