Self-adaptive isogeometric spatial discretisations of the first and second-order forms of the neutron transport equation with dual-weighted residual error measures and diffusion acceleration
File(s)
Author(s)
Wilson, Seth G.
Type
Thesis
Abstract
As implemented in a new modern-Fortran code, NURBS-based isogeometric analysis (IGA) spatial discretisations and self-adaptive mesh refinement (AMR) algorithms are developed in the application to the first-order and second-order forms of the neutron transport equation (NTE).
These AMR algorithms are shown to be computationally efficient and numerically accurate when compared to standard approaches. IGA methods are very competitive and offer certain unique advantages over standard finite element methods (FEM), not least of all because the numerical analysis is performed over an exact representation of the underlying geometry, which is generally available in some computer-aided design (CAD) software description. Furthermore, mesh refinement can be performed within the analysis program at run-time, without the need to revisit any ancillary mesh generator. Two error measures are described for the IGA-based AMR algorithms, both of which can be employed in conjunction with energy-dependent meshes. The first heuristically minimises any local contributions to the global discretisation error, as per some appropriate user-prescribed norm. The second employs duality arguments to minimise important local contributions to the error as measured in some quantity of interest; this is commonly known as a dual-weighted residual (DWR) error measure and it demands the solution to both the forward (primal) and the adjoint (dual) NTE.
Finally, convergent and stable diffusion acceleration and generalised minimal residual (GMRes) algorithms, compatible with the aforementioned AMR algorithms, are introduced to accelerate the convergence of the within-group self-scattering sources for scattering-dominated problems for the first and second-order forms of the NTE. A variety of verification benchmark problems are analysed to demonstrate the computational performance and efficiency of these acceleration techniques.
These AMR algorithms are shown to be computationally efficient and numerically accurate when compared to standard approaches. IGA methods are very competitive and offer certain unique advantages over standard finite element methods (FEM), not least of all because the numerical analysis is performed over an exact representation of the underlying geometry, which is generally available in some computer-aided design (CAD) software description. Furthermore, mesh refinement can be performed within the analysis program at run-time, without the need to revisit any ancillary mesh generator. Two error measures are described for the IGA-based AMR algorithms, both of which can be employed in conjunction with energy-dependent meshes. The first heuristically minimises any local contributions to the global discretisation error, as per some appropriate user-prescribed norm. The second employs duality arguments to minimise important local contributions to the error as measured in some quantity of interest; this is commonly known as a dual-weighted residual (DWR) error measure and it demands the solution to both the forward (primal) and the adjoint (dual) NTE.
Finally, convergent and stable diffusion acceleration and generalised minimal residual (GMRes) algorithms, compatible with the aforementioned AMR algorithms, are introduced to accelerate the convergence of the within-group self-scattering sources for scattering-dominated problems for the first and second-order forms of the NTE. A variety of verification benchmark problems are analysed to demonstrate the computational performance and efficiency of these acceleration techniques.
Version
Open Access
Date Issued
2021-03
Date Awarded
2021-12
Copyright Statement
Creative Commons Attribution NonCommercial Licence
License URL
Advisor
Eaton, Matthew
Bluck, Michael
Sponsor
Engineering and Physical Sciences Research Council (EPSRC)
Rolls-Royce Group plc
Grant Number
EP/N509486/1)
Publisher Department
Mechanical Engineering
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)