AN ADAPTIVE FINITE ELEMENT FORMULATION OF THE BOLTZMANN-TYPE NEUTRON TRANSPORT EQUATION

Shaukat, Iqbal (2007) AN ADAPTIVE FINITE ELEMENT FORMULATION OF THE BOLTZMANN-TYPE NEUTRON TRANSPORT EQUATION. Doctoral thesis, Ghulam Ishaq Khan Institute of Engineering Sciences and Technology, Topi.

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Abstract

Adaptive grid refinement strategies have been formulated to solve the even parity Boltzmann transport equation. The application of continuous and discontinuous finite elements for approximating the spatial dependence of neutron angular flux along with the use of spherical harmonics for directional representation was investigated for some novel neutron transport problems. The study of the conventional variational approaches employing finite elements for solving neutron transport equation has shown that such schemes only ensure a global particle balance over the whole system. Adaptive finite elements have been found to be superior not only in enforcing local particle conservation but also in being more suitable for modelling abrupt changes in angular flux. A residual based a posteriori error estimation scheme has been utilized for checking the approximate solutions for various finite element grids. The local particle balance has been considered as an error assessment criterion. To implement the adaptive approach, a computer program has been developed to solve the second order even parity Boltzmann transport equation 'using variational principles for different geometries. The program has a core module, which employs Lagrange polynomials as spatial basis functions for the finite element formulation and Legendre polynomials for the directional dependence of the solution. The core module is called in by the adaptive grid generator to determine local gradients and residuals to explore the possibility of grid refinements in appropriate regions of the problem. The a posteriori error estimation scheme has been implemented in the outer grid refining iteration module. Numerical experiments indicate that local errors are large in regions where the flux gradients are large. A comparison of the spatially adaptive grid refinement approach with that of uniform meshing approach for various benchmark cases, confirms its superiority in greatly enhancing the accuracy of the solution without increasing the number of unknown coefficients. This scheme is then combined with a discontinuous finite element based composite scheme. This has given the added advantage of automatically generating the orders of angular approximations to be used in different elements/regions in the method of composite solutions. A reduction in the local errors of the order of 102 has been achieved using the new approach in some cases

Item Type: Thesis (Doctoral)
Uncontrolled Keywords: boltzmann-type neutron transport equation, even parity boltzmann transport equation, finite elements, neutron angular flux, legendre expansion, scattering kernel, least squares approach, odd parity flux, even parity flux
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Depositing User: Muhammad Khan Khan
Date Deposited: 02 Sep 2016 04:06
Last Modified: 02 Sep 2016 04:06
URI: http://eprints.hec.gov.pk/id/eprint/772

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