Solving the SN neutron transport equation using high order Lax–Friedrichs WENO fast sweeping methods

Dean Wang; Tseelmaa Byambaakhuu; Sebastian Schunert; Zeyun Wu

Solving the S_N neutron transport equation using high order Lax–Friedrichs WENO fast sweeping methods

Dean Wang
, Tseelmaa Byambaakhuu
, Sebastian Schunert
, Zeyun Wu

Nuclear Reactor Technology

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

Recently we have proposed high order Lax–Friedrichs WENO (LF-WENO) fast sweeping methods for solving the SN neutron transport equation and demonstrated their superior performance in terms of accuracy, convergence, and positivity preserving property [1]. It was found in our previous work that LF-WENO3 can achieve better spatial convergence rate than the diamond difference (DD) method; however both methods do not attain their theoretical order of accuracy in spatial discretization because of lack of sufficient smoothness in the solution of the model problem tested. In the present paper, we further investigate the spatial convergence performance of LF-WENO3 for the SN solution based on the manufactured solutions. Numerical results are presented that show the expected third-order spatial convergence rate of LF-WENO3. In addition, we present in detail numerical analysis of the performance of LF-WENO3 for thick diffusive problems in comparison with the DD and step characteristic (SC) schemes.

Original language	English
Title of host publication	International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019
Publisher	American Nuclear Society
Pages	61-72
Number of pages	12
ISBN (Electronic)	9780894487699
State	Published - 2019
Event	2019 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019 - Portland, United States Duration: Aug 25 2019 → Aug 29 2019

Publication series

Name	International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019

Conference

Conference	2019 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019
Country/Territory	United States
City	Portland
Period	08/25/19 → 08/29/19

Keywords

Diffusion limit
LF-WENO
SN

Cite this

Wang, D., Byambaakhuu, T., Schunert, S., & Wu, Z. (2019). Solving the S_N neutron transport equation using high order Lax–Friedrichs WENO fast sweeping methods. In International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019 (pp. 61-72). (International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019). American Nuclear Society.

Wang, Dean ; Byambaakhuu, Tseelmaa ; Schunert, Sebastian et al. / Solving the S_N neutron transport equation using high order Lax–Friedrichs WENO fast sweeping methods. International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019. American Nuclear Society, 2019. pp. 61-72 (International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019).

@inproceedings{dd9662220df14a0abdf63786449ce5bd,

title = "Solving the SN neutron transport equation using high order Lax–Friedrichs WENO fast sweeping methods",

abstract = "Recently we have proposed high order Lax–Friedrichs WENO (LF-WENO) fast sweeping methods for solving the SN neutron transport equation and demonstrated their superior performance in terms of accuracy, convergence, and positivity preserving property [1]. It was found in our previous work that LF-WENO3 can achieve better spatial convergence rate than the diamond difference (DD) method; however both methods do not attain their theoretical order of accuracy in spatial discretization because of lack of sufficient smoothness in the solution of the model problem tested. In the present paper, we further investigate the spatial convergence performance of LF-WENO3 for the SN solution based on the manufactured solutions. Numerical results are presented that show the expected third-order spatial convergence rate of LF-WENO3. In addition, we present in detail numerical analysis of the performance of LF-WENO3 for thick diffusive problems in comparison with the DD and step characteristic (SC) schemes.",

keywords = "Diffusion limit, LF-WENO, SN",

author = "Dean Wang and Tseelmaa Byambaakhuu and Sebastian Schunert and Zeyun Wu",

note = "Publisher Copyright: {\textcopyright} 2019 American Nuclear Society. All rights reserved.; 2019 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019 ; Conference date: 25-08-2019 Through 29-08-2019",

year = "2019",

language = "English",

series = "International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019",

publisher = "American Nuclear Society",

pages = "61--72",

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Wang, D, Byambaakhuu, T, Schunert, S & Wu, Z 2019, Solving the S_N neutron transport equation using high order Lax–Friedrichs WENO fast sweeping methods. in International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019. International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019, American Nuclear Society, pp. 61-72, 2019 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019, Portland, United States, 08/25/19.

Solving the S_N neutron transport equation using high order Lax–Friedrichs WENO fast sweeping methods. / Wang, Dean; Byambaakhuu, Tseelmaa; Schunert, Sebastian et al.
International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019. American Nuclear Society, 2019. p. 61-72 (International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Solving the SN neutron transport equation using high order Lax–Friedrichs WENO fast sweeping methods

AU - Wang, Dean

AU - Byambaakhuu, Tseelmaa

AU - Schunert, Sebastian

AU - Wu, Zeyun

PY - 2019

Y1 - 2019

N2 - Recently we have proposed high order Lax–Friedrichs WENO (LF-WENO) fast sweeping methods for solving the SN neutron transport equation and demonstrated their superior performance in terms of accuracy, convergence, and positivity preserving property [1]. It was found in our previous work that LF-WENO3 can achieve better spatial convergence rate than the diamond difference (DD) method; however both methods do not attain their theoretical order of accuracy in spatial discretization because of lack of sufficient smoothness in the solution of the model problem tested. In the present paper, we further investigate the spatial convergence performance of LF-WENO3 for the SN solution based on the manufactured solutions. Numerical results are presented that show the expected third-order spatial convergence rate of LF-WENO3. In addition, we present in detail numerical analysis of the performance of LF-WENO3 for thick diffusive problems in comparison with the DD and step characteristic (SC) schemes.

AB - Recently we have proposed high order Lax–Friedrichs WENO (LF-WENO) fast sweeping methods for solving the SN neutron transport equation and demonstrated their superior performance in terms of accuracy, convergence, and positivity preserving property [1]. It was found in our previous work that LF-WENO3 can achieve better spatial convergence rate than the diamond difference (DD) method; however both methods do not attain their theoretical order of accuracy in spatial discretization because of lack of sufficient smoothness in the solution of the model problem tested. In the present paper, we further investigate the spatial convergence performance of LF-WENO3 for the SN solution based on the manufactured solutions. Numerical results are presented that show the expected third-order spatial convergence rate of LF-WENO3. In addition, we present in detail numerical analysis of the performance of LF-WENO3 for thick diffusive problems in comparison with the DD and step characteristic (SC) schemes.

KW - Diffusion limit

KW - LF-WENO

KW - SN

UR - https://www.scopus.com/pages/publications/85075347266

M3 - Conference contribution

AN - SCOPUS:85075347266

T3 - International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019

SP - 61

EP - 72

BT - International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019

PB - American Nuclear Society

T2 - 2019 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019

Y2 - 25 August 2019 through 29 August 2019

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Wang D, Byambaakhuu T, Schunert S, Wu Z. Solving the S_N neutron transport equation using high order Lax–Friedrichs WENO fast sweeping methods. In International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019. American Nuclear Society. 2019. p. 61-72. (International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019). Epub 2019 Aug.