A composite nodal finite element for hexagons

Journal Article · Wed Oct 01 04:00:00 EDT 1997 · Nuclear Science and Engineering

OSTI ID:562069

Hennart, J P ^[1]; Mund, E H ^[2]; Valle, E Del ^[3]

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1. Univ. Nacional Autonoma de Mexico, Mexico City (Mexico). Inst. de Investigaciones en Matematicas Aplicadas y en Sistemas
2. Univ. Libre de Bruxelles (Belgium). Service de Metrologie Nucleaire
3. Inst. Politecnico Nacional, Mexico City (Mexico). Escuela Superior de Fisica y Mathematicas

A nodal algorithm for the solution of the multigroup diffusion equations in hexagonal arrays is analyzed. Basically, the method consists of dividing each hexagon into four quarters and mapping the hexagon quarters onto squares. The resulting boundary value problem on a quadrangular domain is solved in primal weak formulation. Nodal finite element methods like the Raviart-Thomas RTk schemes provide accurate analytical expansions of the solution in the hexagons. Transverse integration cannot be performed on the equations in the quadrangular domain as simply as it is usually done on squares because these equations have essentially variable coefficients. However, by considering an auxiliary problem with constant coefficients (on the same quadrangular domain) and by using a preconditioning approach, transverse integration can be performed as for rectangular geometry. A description of the algorithm is given for a one-group diffusion equation. Numerical results are presented for a simple model problem with a known analytical solution and for k{sub eff} evaluations of some benchmark problems proposed in the literature. For the analytical problem, the results indicate that the theoretical convergence orders of RTk schemes (k = 0,1) are obtained, yielding accurate solutions at the expense of a few preconditioning iterations.

• OSTI ID: 562069
• Journal Information: Nuclear Science and Engineering, Journal Name: Nuclear Science and Engineering Journal Issue: 2 Vol. 127; ISSN NSENAO; ISSN 0029-5639
• Country of Publication: United States
• Language: English

Related Subjects

22 GENERAL STUDIES OF NUCLEAR REACTORS
66 PHYSICS
FINITE ELEMENT METHOD
HEXAGONAL CONFIGURATION
MULTIGROUP THEORY
NEUTRON DIFFUSION EQUATION
NODAL EXPANSION METHOD
REACTOR KINETICS