Publications
37 results found
Buchan AG, Pain CC, 2016, An efficient space-angle subgrid scale discretisation of the neutron transport equation, Annals of Nuclear Energy, Vol: 94, Pages: 440-450, ISSN: 1873-2100
Heaney CE, Buchan AG, Pain CC, et al., 2016, A reduced order model for criticality problems in reactor physics varyingcontrol rod settings, Proceedings of the 24 th UK Conference of the Association for Computational Mechanics in Engineering
Dargaville S, Goffin MA, Buchan AG, et al., 2015, Solving the Boltzmann transport equation with multigrid and adaptive space/angle discretisations, ANNALS OF NUCLEAR ENERGY, Vol: 86, Pages: 99-107, ISSN: 0306-4549
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- Citations: 9
Adam A, Buchan AG, Piggott MD, et al., 2015, Adaptive Haar wavelets for the angular discretisation of spectral wave models, Journal of Computational Physics, Vol: 305, Pages: 521-538, ISSN: 1090-2716
A new framework for applying anisotropic angular adaptivity in spectral wave modelling is presented. The angular dimension of the action balance equation is discretised with the use of Haar wavelets, hierarchical piecewise-constant basis functions with compact support, and an adaptive methodology for anisotropically adjusting the resolution of the angular mesh is proposed. This work allows a reduction of computational effort in spectral wave modelling, through a reduction in the degrees of freedom required for a given accuracy, with an automated procedure and minimal cost.
Buchan AG, Calloo AA, Goffin MG, et al., 2015, A POD reduced order model for resolving angular direction in neutron/photon transport problems, JOURNAL OF COMPUTATIONAL PHYSICS, Vol: 296, Pages: 138-157, ISSN: 0021-9991
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- Citations: 65
Xiao D, Fang F, Buchan AG, et al., 2015, Non-intrusive reduced order modelling of the Navier-Stokes equations, Computer Methods in Applied Mechanics and Engineering, Vol: 293, Pages: 522-541, ISSN: 0045-7825
This article presents two new non-intrusive reduced order models based upon proper orthogonal decomposition (POD) for solving the Navier–Stokes equations. The novelty of these methods resides in how the reduced order models are formed, that is, how the coefficients of the POD expansions are calculated. Rather than taking a standard approach of projecting the underlying equations onto the reduced space through a Galerkin projection, here two different techniques are employed. The first method applies a second order Taylor series to calculate the POD coefficients at each time step from the POD coefficients at earlier time steps. The second method uses a Smolyak sparse grid collocation method to calculate the POD coefficients, where again the coefficients at earlier time steps are used as the inputs. The advantage of both approaches are that they are non-intrusive and so do not require modifications to a system code; they are therefore very easy to implement. They also provide accurate solutions for modelling flow problems, and this has been demonstrated by the simulation of flows past a cylinder and within a gyre. It is demonstrated that accuracy relative to the high fidelity model is maintained whilst CPU times are reduced by several orders of magnitude in comparison to high fidelity models.
Goffin MA, Buchan AG, Dargaville S, et al., 2015, Goal-based angular adaptivity applied to a wavelet-based discretisation of the neutral particle transport equation, JOURNAL OF COMPUTATIONAL PHYSICS, Vol: 281, Pages: 1032-1062, ISSN: 0021-9991
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- Citations: 14
Buchan AG, Jewer S, Farrell PE, et al., 2014, Simulating coupled neutron-fluid-heat transfer for the study of unintended operatingscenarios in pressure water reactors using an immersed body modelling technique, NAFEMS
Goffin MA, Buchan AG, Belme AC, et al., 2014, Goal-based angular adaptivity applied to the spherical harmonics discretisation of the neutral particle transport equation, ANNALS OF NUCLEAR ENERGY, Vol: 71, Pages: 60-80, ISSN: 0306-4549
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- Citations: 20
Merton SR, Smedley-Stevenson RP, Pain CC, et al., 2014, Adjoint eigenvalue correction for elliptic and hyperbolic neutron transport problems, PROGRESS IN NUCLEAR ENERGY, Vol: 76, Pages: 1-16, ISSN: 0149-1970
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- Citations: 3
Jewer S, Buchan AG, Pain CC, et al., 2014, An immersed body method for coupled neutron transport and thermal hydraulic simulations of PWR assemblies, ANNALS OF NUCLEAR ENERGY, Vol: 68, Pages: 124-135, ISSN: 0306-4549
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- Citations: 5
Xiao D, Fang F, Buchan AG, et al., 2014, Non-linear model reduction for the Navier-Stokes equations using residual DEIM method, JOURNAL OF COMPUTATIONAL PHYSICS, Vol: 263, Pages: 1-18, ISSN: 0021-9991
Buchan AG, Farrell PE, Gorman GJ, et al., 2014, The immersed body supermeshing method for modelling reactor physics problems with complex internal structures, ANNALS OF NUCLEAR ENERGY, Vol: 63, Pages: 399-408, ISSN: 0306-4549
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- Citations: 5
Ardjmandpour N, Pain CC, Fang F, et al., 2014, Reduced order borehole induction modelling, INTERNATIONAL JOURNAL OF COMPUTATIONAL FLUID DYNAMICS, Vol: 28, Pages: 140-157, ISSN: 1061-8562
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- Citations: 3
Buchan AG, Pain CC, Fang F, et al., 2013, A POD reduced-order model for eigenvalue problems with application to reactor physics, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Vol: 95, Pages: 1011-1032, ISSN: 0029-5981
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- Citations: 51
Baker CMJ, Buchan AG, Pain CC, et al., 2013, Goal based mesh adaptivity for fixed source radiation transport calculations, Annals of Nuclear Energy, Vol: 55, Pages: 169-183, ISSN: 0306-4549
Merton SR, Buchan AG, Pain CC, et al., 2013, An adjoint-based method for improving computational estimates of a functional obtained from the solution of the Boltzmann Transport Equation, ANNALS OF NUCLEAR ENERGY, Vol: 54, Pages: 1-10, ISSN: 0306-4549
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- Citations: 1
Xiao D, Fang F, Du J, et al., 2013, Non-linear Petrov–Galerkin methods for reduced order modelling of the Navier–Stokes equations using a mixed finite element pair, Computer Methods in Applied Mechanics and Engineering, Vol: 255, Pages: 147-157, ISSN: 0045-7825
Buchan AG, Pain CC, Tollit TS, et al., 2013, Simulated spatially dependent transient kinetics analysis of the Oak Ridge Y12 plant criticality excursion, Progress in Nuclear Energy, Vol: 63, Pages: 12-21
In June 1958 an accidental nuclear excursion occurred in the C-1 Wing of building 9212 in a process facility designed to recover enriched Uranium U(93) from various solid wastes. The accident was caused by the inadvertent flow of enriched uranyl nitrate into a 55 gallon drum which established a prompt critical nuclear excursion. Following the initial fission spike the nuclear system oscillated in power. The reaction was eventually terminated by the additional water which was flowing into the drum. The criticality excursion was estimated to have lasted approximately 20 min based upon nearby radiation measurement equipment with an estimated total fission yield of 1.3 × 1018 fissions of which the first fission spike contributed 6 × 1016 fissions.The traces from the radiation measurement devices indicated that most of the fissions occurred in the first 2.8 min, in which case the average power required for the observed fission yield was approximately 220 kW. After the first 2.8 min the system was postulated to have boiled causing a sharp decrease in density and reactivity of the system. This boiling probably reduced the power output from the system to a low level for the final 18 min of the excursion. This paper will aim to investigate the subsequent evolution of the Y12 excursion using the fundamentally based spatially dependent neutron/multiphase CFD kinetics simulation tool - FETCH. The reconstruction of the Y12 excursion using FETCH will follow the evolution of the excursion up until the uranyl nitrate starts to boil. The results of the FETCH simulation are presented and compared against the known measurements of the excursion from the radiation detection instruments located near the drum.
Baker CMJ, Buchan AG, Pain CC, et al., 2013, Multimesh anisotropic adaptivity for the Boltzmann transport equation, Annals of Nuclear Energy, Vol: 53, Pages: 411-426
This article presents a new adaptive finite element based method for the solution of the spatial dimensions of the Boltzmann transport equation. The method applies a curvature based error metric to locate the under and over resolved regions of a solution and this, in turn, is used to guide the refinement and coarsening of the spatial mesh. The error metrics and re-meshing procedures are designed such that they enable anisotropic resolution to form in the mesh should it be appropriate to do so. The adaptive mesh enables the appropriate resolution to be applied throughout the whole domain of a problem and so increase the efficiency of the solution procedure. Another new approach is also described that allows independent adaptive meshes to form for each of the energy group fluxes. The use of independent meshes can significantly improve computational efficiency when solving problems where the different group fluxes require high resolution over different regions. The mesh to mesh interpolation is made possible through the use of a ‘supermeshing’ procedure that ensures the conservation of particles when calculating the group to group scattering sources. Finally it is shown how these methods can be incorporated within a solver to resolve both fixed source and eigenvalue problems. A selection of both fixed source and eigenvalue problems are solved in order to demonstrate the capabilities of these methods.
Goffin MA, Baker CMJ, Buchan AG, et al., 2013, Minimising the error in eigenvalue calculations involving the Boltzmann transport equation using goal-based adaptivity on unstructured meshes, Journal of Computational Physics, Vol: 242, Pages: 726-762
This article presents a method for goal-based anisotropic adaptive methods for the finite element method applied to the Boltzmann transport equation. The neutron multiplication factor, keff, is used as the goal of the adaptive procedure. The anisotropic adaptive algorithm requires error measures for keff with directional dependence. General error estimators are derived for any given functional of the flux and applied to keff to acquire the driving force for the adaptive procedure. The error estimators require the solution of an appropriately formed dual equation. Forward and dual error indicators are calculated by weighting the Hessian of each solution with the dual and forward residual respectively. The Hessian is used as an approximation of the interpolation error in the solution which gives rise to the directional dependence. The two indicators are combined to form a single error metric that is used to adapt the finite element mesh. The residual is approximated using a novel technique arising from the sub-grid scale finite element discretisation. Two adaptive routes are demonstrated: (i) a single mesh is used to solve all energy groups, and (ii) a different mesh is used to solve each energy group. The second method aims to capture the benefit from representing the flux from each energy group on a specifically optimised mesh. The keff goal-based adaptive method was applied to three examples which illustrate the superior accuracy in criticality problems that can be obtained.
Buchan AG, Pain CC, Umpleby AP, et al., 2012, A sub-grid scale finite element agglomeration multigrid method with application to the Boltzmann transport equation, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Vol: 92, Pages: 318-342, ISSN: 0029-5981
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- Citations: 7
Buchan A, Eaton MD, Goddard AJH, et al., 2012, Simulated transient dynamics and heat transfer characteristics of the water boiler nuclear reactor SUPO with cooling coil heat extraction, Annals of nuclear energy, Vol: 48, Pages: 68-83
The term “water boiler” reactor refers to a type of aqueous homogeneous reactor (AHR) that was designed, built and operated by Los Alamos in the 1940s. This was the first type of liquid fuelled reactor and the first to be fuelled with enriched Uranium. For security reasons the term “water boiler” was adopted and three versions were built: LOPO (for low power), HYPO (for high power) and SUPO (for super power) which were spherical shaped reactor vessels. The name was appropriate as the reactors appeared to boil although this was actually due to the release of radiolytic gas bubbles; although SUPO was operated during some studies close to the boiling point of uranyl nitrate. The final water boiler “SUPO” was operated almost daily as a neutron source from 1951 until its deactivation in 1974-23 years of safe, reliable operation. Many of the key neutron measurements needed in the design of the early atomic weapons were made using LOPO, HYPO and SUPO. More recently SUPO has been considered as a benchmark for quasi-steady-state operation of AHRs with internal cooling structures.This paper presents modelling and analysis of the coupled neutronic and fluid time dependent characteristics of the SUPO reactor. In particular the quasi-steady-state dynamics of SUPO have been investigated together with its heat transfer characteristics. In the simulations presented the SUPO reactor is modelled using the spatially dependent neutron/multiphase CFD simulation tool, FETCH, at a quasi-steady-state power of 25 kW. SUPO also possessed a cooling coil system that fed cooling water through the reactor for the extraction of the fission and decay heat. This cooling system, and the heat extraction, is modelled in the simulations using a new sub-modelling approach that is detailed here. The results from this simulation, such as gas fraction, gas generation rate, coolant rate and average temperature, are compared against the available experimental information.
Baker CMJ, Buchan AG, Pain CC, et al., 2012, Quadratic inner element subgrid scale discretisation of the Boltzmann transport equation, Annals of Nuclear Energy, Vol: 45, Pages: 124-137
This paper explores the application of the inner element subgrid scale method to the Boltzmann transport equation using quadratic basis functions. Previously, only linear basis functions for both the coarse scale and the fine scale were considered. This paper, therefore, analyses the advantages of using different coarse and subgrid basis functions for increasing the accuracy of the subgrid scale method. The transport of neutral particle radiation may be described by the Boltzmann transport equation (BTE) which, due to its 7 dimensional phase space, is computationally expensive to resolve. Multi-scale methods offer an approach to efficiently resolve the spatial dimensions of the BTE by separating the solution into its coarse and fine scales and formulating a solution whereby only the computationally efficient coarse scales need to be solved. In previous work an inner element subgrid scale method was developed that applied a linear continuous and discontinuous finite element method to represent the solution’s coarse and fine scale components. This approach was shown to generate efficient and stable solutions, and so this article continues its development by formulating higher order quadratic finite element expansions over the continuous and discontinuous scales. Here it is shown that a solution’s convergence can be improved significantly using higher order basis functions. Furthermore, by using linear finite elements to represent coarse scales in combination with quadratic fine scales, convergence can also be improved with only a modest increase in computational expense.
Nygaard ET, Pain CC, Eaton MD, et al., 2012, Steps Towards Verification and Validation of the FETCH Code for Level 2 Analysis, Design and Optimization of Aqueous Homogeneous Reactors, PHYSOR
Buchan AG, Pain CC, Eaton MD, et al., 2011, Dynamics and heat transfer characteristics of the water boiler reactor - SUPO, International Conference in Nuclear Criticality
Buchan AG, Pain CC, Eaton MD, et al., 2011, Simulated spatially dependent transient kinetics analysis of the oak ridge Y12 Plant criticality excursion, International Conference in Nuclear Criticality, International Conference in Nuclear Criticality
Baker CMJ, Buchan AG, Pain CC, et al., 2011, Anisotropic mesh adaptivity for eigenvalue calculations using energy dependent meshes, International Conference in Nuclear Criticalit
Merton SR, Smedley-Stevenson RP, Pain CC, et al., 2011, An Adjoint Based Scheme for Eigenvalue Error Improvement, International Conference on Mathematics, Computational Methods & Reactor Physics
Buchan AG, Merton SR, Pain CC, et al., 2011, Riemann boundary conditions for the Boltzmann transport equation using arbitrary angular approximations, ANNALS OF NUCLEAR ENERGY, Vol: 38, Pages: 1186-1195, ISSN: 0306-4549
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- Citations: 19
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