Publications
37 results found
Buchan AG, Candy AS, Merton SR, et al., 2010, The Inner-Element Subgrid Scale Finite Element Method for the Boltzmann Transport Equation, NUCLEAR SCIENCE AND ENGINEERING, Vol: 164, Pages: 105-121, ISSN: 0029-5639
This paper is of particular importance to the nuclear community as it offers a new, efficient and accurate method for resolving the spatial dimensions of the radiation transport (RT) equation. Solving the RT equation can be extremely demanding as its discretisation leads to unusually large and computationally expensive systems. This sub-grid model therefore blends an accurate and stable discontinuous Galerkin method within a computationally efficient continuous framework. It is shown to produce accurate and stable approximations that also capture large solution gradients. This can all be achieved whilst reducing the problem size by up to a factor of 20.
Merton SR, Pain CC, Smedley-Stevenson RP, et al., 2009, A non-linear optimal discontinuous Petrov-Galerkin method for stabilising the solution of the transport equation, International Conference on Mathematics, Computational Methods & Reactor Physics
Merton SR, Pain CC, Smedley-Stevenson RP, et al., 2008, Optimal discontinuous finite element methods for the Boltzmann transport equation with arbitrary discretisation in angle, ANNALS OF NUCLEAR ENERGY, Vol: 35, Pages: 1741-1759, ISSN: 0306-4549
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- Citations: 8
Buchan AG, Pain CC, Eaton MD, et al., 2008, Chebyshev spectral hexahedral wavelets on the sphere for angular discretisations of the Boltzmann transport equation, ANNALS OF NUCLEAR ENERGY, Vol: 35, Pages: 1098-1108, ISSN: 0306-4549
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- Citations: 5
Buchan AG, Pain CC, Eaton MD, et al., 2008, Linear and quadratic hexahedral wavelets on the sphere for angular discretizations of the Boltzmann transport equation, NUCLEAR SCIENCE AND ENGINEERING, Vol: 159, Pages: 127-152, ISSN: 0029-5639
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- Citations: 8
Buchan AG, Pain CC, Eaton MD, et al., 2008, Self-adaptive spherical wavelets for angular discretizations of the Boltzmann transport equation, NUCLEAR SCIENCE AND ENGINEERING, Vol: 158, Pages: 244-263, ISSN: 0029-5639
A new method for applying anisotropic resolution in the angular domain of the Boltzmann transport equation is presented. The method builds on our previous work in which two spherical wavelet bases were developed for representing the direction of neutral particle travel. The method proposed here enables these wavelet bases to vary their angular approximations so that fine resolution may be applied only to the areas of the unit sphere (representing the direction of particle travel) that are important. We develop an error measure that operates in conjunction with the wavelet bases to determine this importance. A procedure by which the angular resolution is gradually refined for steady-state problems is also given.The adaptive wavelets are applied to three test problems that demonstrate the ability of the wavelets to resolve complex fluxes with relatively few functions, and to achieve this a particular emphasis is placed on their ability to approximate particle streaming through ducts with voids. It is shown that the wavelets are capable of applying the appropriate resolution (as dictated by the error measure) to the directional component of the angular flux at all spatial positions. This method therefore offers a new and highly efficient adaptive angular approximation method.
Buchan AG, Pain CC, Eaton MD, et al., 2005, Linear and quadratic octahedral wavelets on the sphere for angular discretisations of the Boltzmann transport equation, ANNALS OF NUCLEAR ENERGY, Vol: 32, Pages: 1224-1273, ISSN: 0306-4549
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- Citations: 46
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