TY - GEN
T1 - A posteriori error estimator and AMR for discrete ordinates nodal transport methods
AU - Duo, Jose I.
AU - Azmy, Yousry Y.
AU - Zikatanov, Ludmil T.
N1 - Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2008
Y1 - 2008
N2 - In the development of high fidelity transport solvers, optimization of the use of available computational resources and access to a tool for assessing quality of the solution are key to the success of large-scale nuclear systems' simulation. Error control provides the analyst with a confidence level in the numerical solution and enables for optimization of resources through Adaptive Mesh Refinement (AMR). In this paper, we derive an a posterior error estimator based on the nodal solution of the Arbitrarily High Order Transport Method of the Nodal type (AHOT-N). Furthermore, by making assumptions on the regularity of the solution, we represent the error estimator as a function of computable volume and element-edges residuals. The global L2 error norm is proved to be bound by the estimator. To lighten the computational load, we present a numerical approximation to the aforementioned residuals and split the global norm error estimator into local error indicators. These indicators are used to drive an AMR strategy for the spatial discretization. However, the indicators based on forward solution residuals alone do not bound the cell-wise error. The estimator and AMR strategy are tested in two problems featuring strong heterogeneity and highly transport streaming regime with strong flux gradients. The results show that the error estimator indeed bounds the global error norms and that the error indicator follows the cell-error's spatial distribution pattern closely. The AMR strategy proves beneficial to optimize resources, primarily by reducing the number of discrete variables unknowns solved for to achieve a prescribed solution accuracy in global L2 error norm. Likewise, AMR achieves higher accuracy compared to uniform refinement when resolving sharp flux gradients, for the same number of unknowns.
AB - In the development of high fidelity transport solvers, optimization of the use of available computational resources and access to a tool for assessing quality of the solution are key to the success of large-scale nuclear systems' simulation. Error control provides the analyst with a confidence level in the numerical solution and enables for optimization of resources through Adaptive Mesh Refinement (AMR). In this paper, we derive an a posterior error estimator based on the nodal solution of the Arbitrarily High Order Transport Method of the Nodal type (AHOT-N). Furthermore, by making assumptions on the regularity of the solution, we represent the error estimator as a function of computable volume and element-edges residuals. The global L2 error norm is proved to be bound by the estimator. To lighten the computational load, we present a numerical approximation to the aforementioned residuals and split the global norm error estimator into local error indicators. These indicators are used to drive an AMR strategy for the spatial discretization. However, the indicators based on forward solution residuals alone do not bound the cell-wise error. The estimator and AMR strategy are tested in two problems featuring strong heterogeneity and highly transport streaming regime with strong flux gradients. The results show that the error estimator indeed bounds the global error norms and that the error indicator follows the cell-error's spatial distribution pattern closely. The AMR strategy proves beneficial to optimize resources, primarily by reducing the number of discrete variables unknowns solved for to achieve a prescribed solution accuracy in global L2 error norm. Likewise, AMR achieves higher accuracy compared to uniform refinement when resolving sharp flux gradients, for the same number of unknowns.
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M3 - Conference contribution
AN - SCOPUS:79953855891
SN - 9781617821219
T3 - International Conference on the Physics of Reactors 2008, PHYSOR 08
SP - 477
EP - 484
BT - International Conference on the Physics of Reactors 2008, PHYSOR 08
PB - Paul Scherrer Institut
T2 - International Conference on the Physics of Reactors 2008, PHYSOR 08
Y2 - 14 September 2008 through 19 September 2008
ER -