Computer codes involving neutron transport theory for nuclear engineering applications always require verification to assess improvement. Generally, analytical and semi-analytical benchmarks are desirable, since they are capable of high precision solutions to provide accurate standards of comparison. However, these benchmarks often involve relatively simple problems, usually assuming a certain degree of abstract modeling. In the present work, we show how semi-analytical equivalent benchmarks can be numerically generated using convergence acceleration. Specifically, we investigate the error behavior of a 1D spatial finite difference scheme for the multigroup (MG) steady-state neutron diffusion equation in plane geometry. Since solutions depending on subsequent discretization can be envisioned as terms of an infinite sequence converging to the true solution, extrapolation methods can accelerate an iterative process to obtain the limit before numerical instability sets in. The obtained results have been compared to the analytical solution to the 1D multigroup diffusion equation when available, using FORTRAN as the computational language. Finally, a slowing down problem has been solved using a cascading source update, showing how a finite difference scheme performs for ultra-fine groups (104 groups) in a reasonable computational time using convergence acceleration.

Converged accelerated finite difference scheme for the multigroup neutron diffusion equation / Terranova N.; Mostacci D.; Ganapol B.D.. - CD-ROM. - 3:(2013), pp. 2088-2102. (Intervento presentato al convegno International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2013 tenutosi a Sun Valley, ID, usa nel 2013).

Converged accelerated finite difference scheme for the multigroup neutron diffusion equation

Terranova N.;Mostacci D.;
2013

Abstract

Computer codes involving neutron transport theory for nuclear engineering applications always require verification to assess improvement. Generally, analytical and semi-analytical benchmarks are desirable, since they are capable of high precision solutions to provide accurate standards of comparison. However, these benchmarks often involve relatively simple problems, usually assuming a certain degree of abstract modeling. In the present work, we show how semi-analytical equivalent benchmarks can be numerically generated using convergence acceleration. Specifically, we investigate the error behavior of a 1D spatial finite difference scheme for the multigroup (MG) steady-state neutron diffusion equation in plane geometry. Since solutions depending on subsequent discretization can be envisioned as terms of an infinite sequence converging to the true solution, extrapolation methods can accelerate an iterative process to obtain the limit before numerical instability sets in. The obtained results have been compared to the analytical solution to the 1D multigroup diffusion equation when available, using FORTRAN as the computational language. Finally, a slowing down problem has been solved using a cascading source update, showing how a finite difference scheme performs for ultra-fine groups (104 groups) in a reasonable computational time using convergence acceleration.
2013
International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2013
2088
2102
Converged accelerated finite difference scheme for the multigroup neutron diffusion equation / Terranova N.; Mostacci D.; Ganapol B.D.. - CD-ROM. - 3:(2013), pp. 2088-2102. (Intervento presentato al convegno International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2013 tenutosi a Sun Valley, ID, usa nel 2013).
Terranova N.; Mostacci D.; Ganapol B.D.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/913058
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