Convergence Analysis of the Nonlinear Coarse-Mesh Finite Difference Method for One-Dimensional Fixed-Source Neutron Diffusion Problem

Journal Article · Tue Jun 15 04:00:00 EDT 2004 · Nuclear Science and Engineering

DOI:https://doi.org/10.13182/NSE03-64· OSTI ID:20804934

Lee, Deokjung ^[1]; Downar, Thomas J ^[1]; Kim, Yonghee ^[2]

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1. Purdue University (United States)
2. Korea Atomic Energy Research Institute (Korea, Republic of)

The convergence rates of the nonlinear coarse-mesh finite difference (CMFD) method and the coarse-mesh rebalance (CMR) method are derived analytically for one-dimensional, one-group solutions of the fixed-source diffusion problem in a nonmultiplying infinite homogeneous medium. The derivation was performed by linearizing the nonlinear algorithm and by applying Fourier error analysis to the linearized algorithm. The mesh size measured in units of the diffusion length is shown to be a dominant parameter for the convergence rate and for the stability of the iterative algorithms. For a small mesh size problem, the nonlinear CMFD is shown to be a more effective acceleration method than CMR. Both CMR and two-node CMFD algorithms are shown to be unconditionally stable. However, the one-node CMFD becomes unstable for large mesh sizes. To remedy this instability, an underrelaxation of the current correction factor for the one-node CMFD method is successfully introduced, and the domain of stability is significantly expanded. Furthermore, the optimum underrelaxation parameter is analytically derived, and the one-node CMFD with the optimum relaxation is shown to be unconditionally stable.

• OSTI ID: 20804934
• Journal Information: Nuclear Science and Engineering, Journal Name: Nuclear Science and Engineering Journal Issue: 2 Vol. 147; ISSN NSENAO; ISSN 0029-5639
• Country of Publication: United States
• Language: English

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ACCELERATION
ALGORITHMS
CONVERGENCE
CORRECTIONS
DIFFUSION
DIFFUSION LENGTH
FINITE DIFFERENCE METHOD
NEUTRON DIFFUSION EQUATION
NONLINEAR PROBLEMS
ONE-DIMENSIONAL CALCULATIONS
STABILITY