Spatial adaptivity of the SAAF and Weighted Least Squares (WLS) forms of the neutron transport equation using constraint based, locally refined, isogeometric analysis (IGA) with dual weighted residual (DWR) error measures
| Autor: | J. Kópházi, C. Latimer, Ryan G. McClarren, Matthew D. Eaton |
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| Přispěvatelé: | Engineering & Physical Science Research Council (EPSRC), Engineering & Physical Science Research Council (E, Engineering and Physical Sciences Research Council, Rolls-Royce Plc |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Neutron transport
Technology Local refinement Physics and Astronomy (miscellaneous) Discretization Computer science SAAF Degrees of freedom (statistics) Nuclear physics 010103 numerical & computational mathematics Isogeometric analysis Adjoint 01 natural sciences Projection (linear algebra) 09 Engineering neutron transport WLS Applied mathematics 0101 mathematics 01 Mathematical Sciences Numerical Analysis Science & Technology 02 Physical Sciences Adaptive mesh refinement Physics Applied Mathematics exact geometry Computer Science Applications 010101 applied mathematics Method of mean weighted residuals Physics Mathematical Computational Mathematics Rate of convergence Modeling and Simulation Physical Sciences Computer Science Isogeometric Analysis Computer Science Interdisciplinary Applications |
| DOI: | 10.5281/zenodo.4108666 |
| Popis: | This paper describes a methodology that enables NURBS (Non-Uniform Rational B-spline) based Isogeometric Analysis (IGA) to be locally refined. The methodology is applied to continuous Bubnov-Galerkin IGA spatial discretisations of second-order forms of the neutron transport equation. In particular this paper focuses on the self-adjoint angular flux (SAAF) and weighted least squares (WLS) equations. Local refinement is achieved by constraining degrees of freedom on interfaces between NURBS patches that have different levels of spatial refinement. In order to effectively utilise constraint based local refinement, adaptive mesh refinement (AMR) algorithms driven by a heuristic error measure or forward error indicator (FEI) and a dual weighted residual (DWR) or goal-based error measure (WEI) are derived. These utilise projection operators between different NURBS meshes to reduce the amount of computational effort required to calculate the error indicators. In order to apply the WEI to the SAAF and WLS second-order forms of the neutron transport equation the adjoint of these equations are required. The physical adjoint formulations are derived and the process of selecting source terms for the adjoint neutron transport equation in order to calculate the error in a given quantity of interest (QoI) is discussed. Several numerical verification benchmark test cases are utilised to investigate how the constraint based local refinement affects the numerical accuracy and the rate of convergence of the NURBS based IGA spatial discretisation. The nuclear reactor physics verification benchmark test cases show that both AMR algorithms are superior to uniform refinement with respect to accuracy per degree of freedom. Furthermore, it is demonstrated that for global QoI the FEI driven AMR and WEI driven AMR produce similar results. However, if local QoI are desired then WEI driven AMR algorithm is more computationally efficient and accurate per degree of freedom. This work was also funded under: EPSRC Grant No: EP/R511547/1 (https://gow.epsrc.ukri.org/NGBOViewGrant.aspx?GrantRef=EP/R511547/1) EPSRC Grant No: EP/K503733/1 (https://gow.epsrc.ukri.org/NGBOViewGrant.aspx?GrantRef=EP/K503733/1) |
| Databáze: | OpenAIRE |
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