Theory and Methodology

• 1. Introduction
  • 1.1. References
• 2. Method of Characteristics
  • 2.1. Introduction to the Boltzmann Equation
  • 2.2. The Characteristic Transformation
  • 2.3. The Multi-Group Energy Approximation
  • 2.4. The Discrete Ordinates Approximation
  • 2.5. The Isotropic Scattering Approximation
  • 2.6. The Flat Source Region Approximation
  • 2.7. The Linear Source Region Approximation
  • 2.8. The Constant Cross-Section Approximation
  • 2.9. The Integrating Factor Solution
  • 2.10. The Track Area Approximation
  • 2.11. Projection from the Azimuthal Plane
  • 2.12. References
• 3. Eigenvalue Calculations
  • 3.1. MOC Iteration Scheme
  • 3.2. Source Update Algorithm
  • 3.3. Transport Sweep Algorithm
  • 3.4. Source Convergence Criterion
  • 3.5. Exponential Evaluation Method
  • 3.6. References
• 4. Constructive Solid Geometry
  • 4.1. CSG Formulation
  • 4.2. References
• 5. Track Generation
  • 5.1. Cyclic Tracks
  • 5.2. Modular Ray Tracing
  • 5.3. Azimuthal Angle Quadrature
  • 5.4. Polar Angle Quadrature
  • 5.5. Spatial Quadrature
  • 5.6. Ray Tracing
  • 5.7. On-The-Fly Ray Tracing
  • 5.8. References
• 6. Parallelization of the Method of Characteristics for neutron transport
• 7. Coarse Mesh Finite Difference Acceleration
  • 7.1. Cross Section Generation
  • 7.2. Applying the Finite Difference Approximation
  • 7.3. Introduction to nonlinear diffusion correction factors
  • 7.4. Treatment of optically thick regions
  • 7.5. Treatment of coarse mesh cell corner crossings
  • 7.6. Matrix form of CMFD method
  • 7.7. CMFD Accelerated MOC Algorithm
  • 7.8. Quadratic axial interpolation
  • 7.9. Domain decomposition
  • 7.10. References
• 8. Krylov Subspace Methods