A spatially variant rebalancing method for discrete-ordinates transport equation. (November 2019)

• Record Type: Journal Article
• Authors: Ford, Wesley; Masiello, Emiliano; Calvin, Christophe; Févotte, François; Lathuilière, Bruno
• Is Part Of: Annals of nuclear energy. Volume 133(2019)
• Page Start: 589
• Page End: 602
• Publication Date: 2019-11
• Subjects: Discrete-ordinates transport equation -- Non-linear acceleration -- Stability analysis -- Fourier analysis -- Jacobian; Nuclear energy -- Periodicals; Nuclear engineering -- Periodicals; 621.4805
• DOI: 10.1016/j.anucene.2019.06.046
• Languages: English
• ISSNs: 0306-4549

Abstract

Highlights: A new class of non-linear acceleration methods has been created (SVRM). The stability of SVRM is shown through a spectral radius and Fourier analysis. The simplified numerical benchmark indicates a significant effectiveness advantage. Abstract: In this paper we propose a new non-linear technique for accelerating the source iterations of the discrete-ordinates transport equation. The acceleration method, called Spatially Variant Rebalancing Method (SVRM), is based on the computation of the zeroth and first order spatial variation of the neutron balance equation. The non-linear acceleration is applied to the method of characteristics (MOC) with a step-approximation of the source. The new acceleration is meant to catch the high-order variation of the neutron flux within the spatial mesh. The paper proposes a numerical analysis of the technique based on the explicit computation of the Jacobian. The latter is analyzed with both spectral and Fourier analysis (Hong et al., 2010). Also, a comparison of the new method against CMFD (Smith, 1983 ), DSA (Larsen, 1982), and BPA (Adams et al., 1988) has been done for a parametrized heterogeneous problem, in order to study the performance of SVRM in different transport regimes. The analysis of SVRM has been constrained to plane geometries.