Abstract
Advancement in multiphysics simulation has motivated interest in availability of analytic and semi-analytic benchmark solutions. These solutions are sought because they can be used to assess the accuracy of complicated numerical schemes necessary to simulate coupled physics systems. While there exist analytic solutions for fixed-source problems, benchmark-quality eigenvalue solutions are of interest because eigenvalue problems more closely align with analyses undertaken with coupled solvers. This paper extends a fixed-source benchmark, the Doppler Slab benchmark, to the eigenvalue case. A novel solution for this benchmark is derived. Numerical implementation of the benchmark is demonstrated through verification of numerical computation of the power reactivity coefficient.
Highlights
Interest in the characterization of the stability and the convergence characteristics of coupled-physics simulations for nuclear engineering applications has motivated the development of analytic, semi-analytic, and method of manufactured solution benchmarks, such as [1,2,3,4,5,6]
This paper extends the Doppler Slab benchmark to an eigenvalue problem
The eigenvalue extension was solved semi-analytically with inverse-root Doppler broadening to yield an expression for eigenvalue (%„ ) as a function of the boundary and initial conditions of the problem
Summary
Interest in the characterization of the stability and the convergence characteristics of coupled-physics simulations for nuclear engineering applications has motivated the development of analytic, semi-analytic, and method of manufactured solution benchmarks, such as [1,2,3,4,5,6]. While each of these benchmarks’ applicability to their relevant physics considerations has been demonstrated, the utility of Kooreman and Griesheimer’s work is twofold. The solution can best be characterized as semi-analytic rather than fully analytic because expressions for flux and eigenvalue are dependent upon a parameter that must be found via root-finding algorithms Since these techniques can give results to any desired precision, the eigenvalue extension of the Doppler Slab problem is a high-precision benchmark applicable to neutron transport codes coupled with thermal conduction feedback. A coupled code system with the in-house Monte Carlo code MC21 [8] and an in-house thermal conduction solver is used to numerically evaluate the benchmark through evaluation of the power reactivity coefficient via a brute-force method
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