A symmetric interior-penalty discontinuous Galerkin isogeometric analysis spatial discretization of the self-adjoint angular flux form of the neutron transport equation

• Published in: Computer methods in applied mechanics and engineering Vol. 432; p. 117414
• Main Authors: Wilson, S.G., Eaton, M.D., Kópházi, J.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.12.2024
• Subjects: Discontinuous galerkin; Discrete ordinates (SN); Interior-penalty scheme; Isogeometric analysis; Multi-group neutron transport equation; Self-Adjoint Angular Flux (SAAF); Isogeometric analysis; Self-Adjoint Angular Flux (SAAF); Discrete ordinates (SN); Interior-penalty scheme; Multi-group neutron transport equation; Discontinuous galerkin
• ISSN: 0045-7825
• DOI: 10.1016/j.cma.2024.117414

This paper presents the first application of a symmetric interior-penalty discontinuous Galerkin isogeometric analysis (SIP-DG-IGA) spatial discretization to the self-adjoint angular flux (SAAF) form of the multi-group neutron transport equation. The penalty parameters are determined, for general element types, from a mathematically rigorous coercivity analysis of the bilinear form. The proposed scheme produces a compact spatial discretization stencil. It also yields symmetric positive-definite (SPD) matrices, which can be efficiently solved using pre-conditioned conjugate gradient (PCG) solution algorithms. The proposed discretization scheme is verified using the method of manufactured solutions (MMS) and several nuclear reactor physics benchmark verification test cases. For sufficiently smooth elliptic problems, the proposed spatial discretization can exploit higher-order continuity, or k-refinement, of the NURBS basis to consistently yield greater numerical accuracy per degree of freedom (DoF) than standard h-refinement. Since this is a discontinuous scheme, it can also accurately model significant changes in the neutron scalar flux that may occur near the material interfaces of heterogeneous problems.