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Title: Multiscale Capability in Rattlesnake using Contiguous Discontinuous Discretization of Self-Adjoint Angular Flux Equation

Abstract

In this report, we present a new upwinding scheme for the multiscale capability in Rattlesnake, the MOOSE based radiation transport application. Comparing with the initial implementation of multiscale utilizing Lagrange multipliers to impose strong continuity of angular flux on interface of in-between subdomains, this scheme does not require the particular domain partitioning. This upwinding scheme introduces discontinuity of angular flux and resembles the classic upwinding technique developed for solving first order transport equation using discontinuous finite element method (DFEM) on the subdomain interfaces. Because this scheme restores the causality of radiation streaming on the interfaces, significant accuracy improvement can be observed with moderate increase of the degrees of freedom comparing with the continuous method over the entire solution domain. Hybrid SN-PN is implemented and tested with this upwinding scheme. Numerical results show that the angular smoothing required by Lagrange multiplier method is not necessary for the upwinding scheme.

Authors:
 [1];  [2];  [2]
  1. Texas A & M Univ., College Station, TX (United States)
  2. Idaho National Lab. (INL), Idaho Falls, ID (United States)
Publication Date:
Research Org.:
Idaho National Lab. (INL), Idaho Falls, ID (United States)
Sponsoring Org.:
USDOE Office of Nuclear Energy (NE)
OSTI Identifier:
1364491
Report Number(s):
INL/EXT-16-39793
TRN: US1703367
DOE Contract Number:
AC07-05ID14517
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
22 GENERAL STUDIES OF NUCLEAR REACTORS; FINITE ELEMENT METHOD; COMPARATIVE EVALUATIONS; DEGREES OF FREEDOM; RADIATION STREAMING; RADIATION TRANSPORT; multiscale; Rattlesnake; TREAT

Citation Formats

Zheng, Weixiong, Wang, Yaqi, and DeHart, Mark D. Multiscale Capability in Rattlesnake using Contiguous Discontinuous Discretization of Self-Adjoint Angular Flux Equation. United States: N. p., 2016. Web. doi:10.2172/1364491.
Zheng, Weixiong, Wang, Yaqi, & DeHart, Mark D. Multiscale Capability in Rattlesnake using Contiguous Discontinuous Discretization of Self-Adjoint Angular Flux Equation. United States. doi:10.2172/1364491.
Zheng, Weixiong, Wang, Yaqi, and DeHart, Mark D. Thu . "Multiscale Capability in Rattlesnake using Contiguous Discontinuous Discretization of Self-Adjoint Angular Flux Equation". United States. doi:10.2172/1364491. https://www.osti.gov/servlets/purl/1364491.
@article{osti_1364491,
title = {Multiscale Capability in Rattlesnake using Contiguous Discontinuous Discretization of Self-Adjoint Angular Flux Equation},
author = {Zheng, Weixiong and Wang, Yaqi and DeHart, Mark D.},
abstractNote = {In this report, we present a new upwinding scheme for the multiscale capability in Rattlesnake, the MOOSE based radiation transport application. Comparing with the initial implementation of multiscale utilizing Lagrange multipliers to impose strong continuity of angular flux on interface of in-between subdomains, this scheme does not require the particular domain partitioning. This upwinding scheme introduces discontinuity of angular flux and resembles the classic upwinding technique developed for solving first order transport equation using discontinuous finite element method (DFEM) on the subdomain interfaces. Because this scheme restores the causality of radiation streaming on the interfaces, significant accuracy improvement can be observed with moderate increase of the degrees of freedom comparing with the continuous method over the entire solution domain. Hybrid SN-PN is implemented and tested with this upwinding scheme. Numerical results show that the angular smoothing required by Lagrange multiplier method is not necessary for the upwinding scheme.},
doi = {10.2172/1364491},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Thu Sep 01 00:00:00 EDT 2016},
month = {Thu Sep 01 00:00:00 EDT 2016}
}

Technical Report:

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  • Nonlinear acceleration of a continuous finite element (CFE) discretization of the transport equation requires a modification of the transport solution in order to achieve local conservation, a condition used in nonlinear acceleration to define the stopping criterion. In this work we implement a coarse-mesh finite difference acceleration for a CFE discretization of the second-order self-adjoint angular flux (SAAF) form of the transport equation and use a postprocessing to enforce local conservation. Numerical results are given for one-group source calculations of one-dimensional slabs. We also give a novel formal derivation of the boundary conditions for the SAAF.
  • Nonlinear acceleration of a continuous finite element (CFE) discretization of the transport equation requires a modification of the transport solution in order to achieve local conservation, a condition used in nonlinear acceleration to define the stopping criterion. In this work we implement a coarse-mesh finite difference acceleration for a CFE discretization of the second-order self adjoint angular flux (SAAF) form of the transport equation and use a post processing to enforce local conservation. Numerical results are given for one-group source calculations of one-dimensional slabs. We also give a formal derivation of the boundary conditions for the SAAF. (authors)
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  • In this paper, we study the Least-Squares (LS) PN form of the transport equation compatible with voids in the context of Continuous Finite Element Methods (CFEM).We first deriveweakly imposed boundary conditions which make the LS weak formulation equivalent to the Self-Adjoint Angular Flux (SAAF) variational formulation with a void treatment, in the particular case of constant cross-sections and a uniform mesh. We then implement this method in Rattlesnake with the Multiphysics Object Oriented Simulation Environment (MOOSE) framework using a spherical harmonics (PN) expansion to discretize in angle. We test our implementation using the Method of Manufactured Solutions (MMS) and findmore » the expected convergence behavior both in angle and space. Lastly, we investigate the impact of the global non-conservation of LS by comparing the method with SAAF on a heterogeneous test problem.« less
  • In this paper, we study the Least-Squares (LS) PN form of the transport equation compatible with voids [1] in the context of Continuous Finite Element Methods (CFEM).We first deriveweakly imposed boundary conditions which make the LS weak formulation equivalent to the Self-Adjoint Angular Flux (SAAF) variational formulation with a void treatment [2], in the particular case of constant cross-sections and a uniform mesh. We then implement this method in Rattlesnake with the Multiphysics Object Oriented Simulation Environment (MOOSE) framework [3] using a spherical harmonics (PN) expansion to discretize in angle. We test our implementation using the Method of Manufactured Solutionsmore » (MMS) and find the expected convergence behavior both in angle and space. Lastly, we investigate the impact of the global non-conservation of LS by comparing the method with SAAF on a heterogeneous test problem.« less