A Continuous-Discontinuous Hybrid Finite Element Method for S{sub N} Transport

Journal Article · Sat Jul 01 04:00:00 EDT 2017 · Transactions of the American Nuclear Society

OSTI ID:23047503

Zheng, Weixiong; McClarren, Ryan G. ^[1]

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1. Nuclear Engineering, Texas A and M University, College Station, TX 77843-3133 (United States)

Particle transport phenomenon for neutral particles, such as neutrons and photons, is governed by the linear Boltzmann equation, which is a first-order partial differential equation (PDE). In order to solve the transport equation, discontinuous finite element method (DFEM) is heavily developed. However, the large memory consumption due to the extra degrees of freedom is problematic in multi-D calculations. Another path is to recast the transport equation to a second-order form, such as the well-known self-adjoint angular flux equation (SAAF) and the even parity equations, and spatially discretize the equation using continuous finite element method (CFEM). Yet, such forms generally have problems in void situation as the streaming operator contains a 1/σ{sub t} term and becomes singular in void, which draws numerous efforts on developing void-treatment methods. An intuition to mitigate the shortcomings of both methods is then to develop a method that utilizes DFEM in part of the problem where CFEM has issues while in the other part, CFEM is employed to avoid DFEM's high cost. In this work, we present a novel continuous-discontinuous finite element method (CDFEM) for solving the discrete-ordinates (S{sub N}) transport equations. We perform the hybridization between 1/σ{sub t}-weighted least-squares finite element methods (1/σ{sub t}-LSFEM), with continuous basis functions, and first-order solver. Different solvers are defined in different regions, or subdomains, of the problem. The resulting scheme is such that CFEM-SAAF is performed in subdomains with continuous basis functions while upwinding based DFEM solver is utilized in subdomains with discontinuous basis functions. The connection between subdomains is through an upwinding operation on the interface, which can be performed via the sweep procedure. A foreseeable benefit is such a scheme is compatible with void as first-order DFEM solver can be used in void. On the other hand, as DFEM is only used in part of the problem, CDFEM can effectively avoid the notorious memory consumption of DFEM in multi-D calculation for the future work.

• OSTI ID: 23047503
• Journal Information: Transactions of the American Nuclear Society, Journal Name: Transactions of the American Nuclear Society Vol. 116; ISSN 0003-018X
• Country of Publication: United States
• Language: English

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
97 MATHEMATICS AND COMPUTING
BOLTZMANN EQUATION
DEGREES OF FREEDOM
DISCRETE ORDINATE METHOD
FINITE ELEMENT METHOD
LEAST SQUARE FIT
NEUTRAL PARTICLES
NEUTRONS
OPERATION
PHOTONS
TRANSPORT THEORY
VOIDS