Theory Manual

• 1. Background on the Linear Boltzmann Equation
  • 1.1. Definitions
  • 1.2. The Linear Boltzmann Equation
  • 1.3. Boundary Conditions
  • 1.4. Initial Conditions
  • 1.5. Expansion of the Angle Redistribution Term
  • 1.6. Short summary of Transport Equations Solved in OpenSn
  • 1.7. Streaming Term in Cartesian and Curvilinear Coordinate Systems
  • 1.8. References
• 2. Phase-space Discretization
  • 2.1. Energy Discretization
  • 2.2. Angle Discretization (the Sn method)
  • 2.3. Spatial Discretization
  • 2.4. References
• 3. Time Discretization
  • 3.1. Theta scheme
  • 3.2. Delayed-neutron precursors
  • 3.3. Particle balance
  • 3.4. Initial state
• 4. Multigroup Cross-Section Data
• 5. Outcome of a Simulation: Particle Distribution, Reaction Rates, and Leakage Rates
• 6. Iterative Solution Algorithms
  • 6.1. Multigroup Solution Process: Background
  • 6.2. Source Iteration and Krylov Solvers
  • 6.3. Within-group Acceleration
  • 6.4. Thermal Upscattering Acceleration
  • 6.5. Power Iterations
  • 6.6. Acceleration of Power Iterations
  • 6.7. Coarse-Mesh Finite Difference Acceleration
  • 6.8. Uncollided-flux Treatment
  • 6.9. References
• 7. Parallel Sweeps
  • 7.1. Introduction
  • 7.2. Aggregation
  • 7.3. Partitioning and Scheduling
  • 7.4. References
• 8. Adjoint Flux Formalism
  • 8.1. Discrete adjoint formulation
  • 8.2. Theory: adjoint response identity
  • 8.3. Discrete implementation
• 9. Continuous Slowing-Down Approximation
  • 9.1. Conventions
  • 9.2. Continuous-energy equation
  • 9.3. Within-group representation
  • 9.4. Slowing-down density at group edges
  • 9.5. Augmented local sweep
  • 9.6. Deposited-energy fields
  • 9.7. Charge deposition
  • 9.8. Particle balance
  • 9.9. Energy balance