Development of a finite volume inter-cell polynomial expansion method for the neutron diffusion equation. Issue 8 (2nd August 2016)

• Record Type: Journal Article
• Authors: Bernal, Álvaro; Roman, Jose E.; Miró, Rafael; Ginestar, Damián; Verdú, Gumersindo
• Is Part Of: Journal of nuclear science and technology. Volume 53:Issue 8(2016)
• Page Start: 1212
• Page End: 1223
• Publication Date: 2016-08-02
• Subjects: neutron diffusion equation -- finite volume method -- polynomial expansion -- steady state; Nuclear engineering -- Periodicals; Nuclear physics -- Periodicals; Nuclear energy -- Periodicals; 621.4805
• DOI: 10.1080/00223131.2015.1102661
• Languages: English
• ISSNs: 0022-3131

Abstract

Abstract : Heterogeneous nuclear reactors require numerical methods to solve the neutron diffusion equation (NDE) to obtain the neutron flux distribution inside them, by discretizing the heterogeneous geometry in a set of homogeneous regions. This discretization requires additional equations at the inner faces of two adjacent cells: neutron flux and current continuity, which imply an excess of equations. The finite volume method (FVM) is suitable to be applied to NDE, because it can be easily applied to any mesh and it is typically used in the transport equations due to the conservation of the transported quantity within the volume. However, the gradient and face-averaged values in the FVM are typically calculated as a function of the cell-averaged values of adjacent cells. So, if the materials of the adjacent cells are different, the neutron current condition could not be accomplished. Therefore, a polynomial expansion of the neutron flux is developed in each cell for assuring the accomplishment of the flux and current continuity and calculating both analytically. In this polynomial expansion, the polynomial terms for each cell were assigned previously and the constant coefficients are determined by solving the eigenvalue problem with SLEPc. A sensitivity analysis for determining the best set of polynomial terms is performed.