Imperial College London
Dr Matthew Eaton

DrMatthewEaton

Faculty of Engineering, Department of Mechanical Engineering

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Contact

 

+44 (0)20 7594 7053m.eaton

 
 
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Location

 

657City and Guilds BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Jeffers:2020:10.1080/23324309.2019.1710214,
author = {Jeffers, RS and Kópházi, J and Eaton, MD and Févotte, F and Hülsemann, F and Ragusa, J},
doi = {10.1080/23324309.2019.1710214},
journal = {Journal of Computational and Theoretical Transport},
pages = {51--87},
title = {Goal-based error estimation for the multi-dimensional diamond difference and box discrete ordinate (SN) methods},
url = {http://dx.doi.org/10.1080/23324309.2019.1710214},
volume = {49},
year = {2020}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - Goal-based error estimation due to spatial discretization and adaptive mesh refinement (AMR) has previously been investigated for the one dimensional, diamond difference, discrete ordinate (1-D DD-SN) method for discretizing the Neutron Transport Equation (NTE). This paper investigates the challenges of extending goal-based error estimation to multi-dimensions with supporting evidence provided on 2-D fixed (extraneous) source and Keff eigenvalue (criticality) verification test cases. It was found that extending Hennart’s weighted residual view of the lowest order 1-D DD equations to multi-dimensions gave what has previously been called the box method. This paper shows how the box method can be extended to higher orders. The paper also shows an equivalence between the higher order box methods and the higher order DD methods derived by Hébert et al. Though, less information is retained in the final solution in the latter case. These extensions allow for the definition of dual weighted residual (DWR) error estimators in multi-dimensions for the DD and box methods. However, they are not applied to drive AMR in the multi-dimensional case due to the various challenges explained in this paper.
AU  - Jeffers,RS
AU  - Kópházi,J
AU  - Eaton,MD
AU  - Févotte,F
AU  - Hülsemann,F
AU  - Ragusa,J
DO  - 10.1080/23324309.2019.1710214
EP  - 87
PY  - 2020///
SN  - 2332-4309
SP  - 51
TI  - Goal-based error estimation for the multi-dimensional diamond difference and box discrete ordinate (SN) methods
T2  - Journal of Computational and Theoretical Transport
UR  - http://dx.doi.org/10.1080/23324309.2019.1710214
UR  - https://www.tandfonline.com/doi/full/10.1080/23324309.2019.1710214
UR  - http://hdl.handle.net/10044/1/76569
VL  - 49
ER  -
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