An Adaptive Approach to Variational Nodal Diffusion Problems

Journal Article · Mon Jan 15 04:00:00 EST 2001 · Nuclear Science and Engineering

OSTI ID:20804683

Hui, Zhang; Lewis, E E ^[1]

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1. Northwestern University (United States)

An adaptive grid method is presented for the solution of neutron diffusion problems in two dimensions. The primal hybrid finite elements employed in the variational nodal method are used to reduce the diffusion equation to a coupled set of elemental response matrices. An a posteriori error estimator is developed to indicate the magnitude of local errors stemming from the low-order elemental interface approximations. An iterative procedure is implemented in which p refinement is applied locally by increasing the polynomial order of the interface approximations. The automated algorithm utilizes the a posteriori estimator to achieve local error reductions until an acceptable level of accuracy is reached throughout the problem domain. Application to a series of X-Y benchmark problems indicates the reduction of computational effort achievable by replacing uniform with adaptive refinement of the spatial approximations.

• OSTI ID: 20804683
• Journal Information: Nuclear Science and Engineering, Journal Name: Nuclear Science and Engineering Journal Issue: 1 Vol. 137; ISSN NSENAO; ISSN 0029-5639
• Country of Publication: United States
• Language: English

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ACCURACY
ALGORITHMS
APPROXIMATIONS
BENCHMARKS
DIFFUSION
ERRORS
INTERFACES
ITERATIVE METHODS
MATHEMATICAL SOLUTIONS
MATRICES
NEUTRON DIFFUSION EQUATION
NEUTRON TRANSPORT
NEUTRON TRANSPORT THEORY
POLYNOMIALS
VARIATIONAL METHODS