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Home / Publications / Journals / Nuclear Science and Engineering / Volume 191 / Number 2

Discontinuous Finite Element Quasi-Diffusion Methods

Dmitriy Y. Anistratov, James S. Warsa

Nuclear Science and Engineering / Volume 191 / Number 2 / August 2018 / Pages 105-120

Technical Paper / dx.doi.org/10.1080/00295639.2018.1450013

Received:November 28, 2017
Accepted:March 5, 2018
Published:July 13, 2018

In this paper, two-level methods for solving transport problems in one-dimensional slab geometry based on the quasi-diffusion (QD) method are developed. A linear discontinuous finite element method (LDFEM) is derived for the spatial discretization of the low-order QD (LOQD) equations. It involves special interface conditions at the cell edges based on the idea of QD boundary conditions (BCs). We consider different kinds of QD BCs to formulate the necessary cell-interface conditions. We develop two-level methods with independent discretization of the high-order transport equation and LOQD equations, where the transport equation is discretized using the method of characteristics and the LDFEM is applied to the LOQD equations. We also formulate closures that lead to the discretization consistent with a LDFEM discretization of the transport equation. The proposed methods are studied by means of test problems formulated with the method of manufactured solutions. Numerical experiments are presented demonstrating the performance of the proposed methods. We also show that the method with independent discretization has the asymptotic diffusion limit.

 
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