




S. No. 
Chapter 
Title of the Chapters 
Page 
Size (KB) 





1 
0 
Contents 

187.82 KB 





2 
1 
Introduction 
18 
145.78 KB 

1.1 
The Importance Of Numerical Methods 
18 

1.2 
Finite Element Method In Neutron Transport 
21 

1.3 
Mesh Adaptivity 
24 

1.4 
Motivation Of The Work 
27 

1.5 
Contribution To The Work 
28 

1.6 
Layout Of Thesis 
29 





3 
2 
Transport Theory 
31 
231.39 KB 

2.1 
Introduction 
31 

2.2 
Introductory Definitions 
32 

2.3 
Derivation Of Particle Transport Equation 
37 

2.4 
Neutron Transport Equation 
41 

2.5 
Boundary Conditions 
42 

2.6 
Legendre Expansion Of The Scattering Kernel 
44 

2.7 
Second Order From Of The Transport Equation 
45 





4 
3 
Variational Treatment Of The Boltzmann Transport Equation 

186.01 KB 

3.1 
Need For A Generalized Least Squares Approach 
49 

3.2 
Generalized Least Squares Approach 
50 

3.3 
A Generalized Least Squares Identity For The First Order Boltzmann Equation 
50 

3.4 
Measures Of Errors Of Approximate Solutions 
52 

3.5 
LeastSquares Functionals 
55 

3.6 
Variational Principles Admitting Continuous Trial Functions 
58 

3.7 
Variational Principles Admitting Discontinuous Trial Functions 
61 

3.8 
The Role Of The Penalty Parameter Î› 
63 





5 
4 
Finite Elements Formulation 
65 
468.6 KB 

4.1 
Introduction 
65 

4.2 
Trial Functions For Directional Dependence Of The Angular Flux 
66 

4.3 
Finite Element Trial Functions For Spatial Domain 
69 

4.4 
Even And Odd Parity Trial Functions 
75 

4.5 
The Discretized Functionals 
76 

4.6 
Derivation Of Odd Parity Flux From Even Parity Flux 
89 

4.7 
Derivation Of Even Parity Flux From Odd Parity Flux 
89 

4.8 
Determination Of Integral Quantities Of Interest 
90 





6 
5 
Adaptive Finite Element Approach 

323.52 KB 

5.1 
Error Estimation 
92 

5.2 
Adaptive Strategies 
94 

5.3 
A Posteriori Error Estimates For Adaptive Grid Refinement Approaches 
97 

5.4 
Computational Aspects And Implementation 
99 

5.5 
Numerical Results And Discussion 
101 





7 
6 
Development Of A Combined Approaches For Spatial Mesh And Angular Approximation Adaptivity 

451.95 KB 

6.1 
Introduction 
111 

6.2 
Composite Solution Case Studies 
113 

6.3 
Adaptive Construction Of Composite Solutions 
128 

6.4 
Numerical Case Studies For Adaptive Composite Approach 
130 





8 
7 
Conclusions And Future Recommendations 

45.86 KB 

7.1 
Conclusions 
136 

7.2 
Future Recommendations 
138 





9 
8 
References 
140 
159.86 KB 

8.1 
Appendix 
151 




