SecondOrder Neutron

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• Second-Order Neutron
• Transport Methods
•  E. E. Lewis
• Northwestern University
• e-lewis_at_northwestern.edu

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Scope

• Multigroup Energy Discretization
• Time-Independent Equation
• Engineering Software Emphasis
• Neutronics Emphasis
• 2nd Order Coupled 1st Order Equations

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Outline

• The Equations
• Some History
• Coupled 2nd Order Diffusion Theory
• Fine Mesh Transport Methods
• Hybrid and Nodal Transport Methods
• Integral Transport Methods
• Present Future Work

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1. First-Order Mixed Equations
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1. Second-Order Equations
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2. Some History

• Analytical Methods Diffusion Theory
• Vladimirov Functional (1963)
• Variational Formulations (1967)
• Finite Elements in Diffusion Methods (1970)
• Finite Elements in Transport Calculation
  (1970s)
• Major Engineering Codes ( 1980s 1990s)
• EVENT, CRONOS, DANTE, VARIANT more

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3. Diffusion Theory
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3. Mixed Equations
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3. Second-Order Equation
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3. Variational Principle
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3. Discretization Finite Elements
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3. Co Spatial Elements
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3. Discretized Functional
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3. Discretized Equations
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4. Even-Parity Transport
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4. Anisotropic Scattering
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4. Anisotropic Scattering
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4. Angular Approximations
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4. Angular Approximations
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4. Pn vs. Sn Ray Effects
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4. Funtional Euler Equations
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4. Spatial Discretization
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4. Reduced Functional
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4. Discretized Equations
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5. Hybrid Nodal Methods
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5. Hybrid Finite Element
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5. Discretized Equations
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5. Even-Parity Nodal Transport
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5. Discretized Equations
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6. Even-Parity Integral Method
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6. Finite Element Discretization
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6. Even-Parity Integral Equations
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7. Current Future Work

• Nodal Finite Subelement Method
• Integral Nodal Finite Subelement Method
• Treatment of vacuums thick pure scattering
  media
• Curvilinear coordinate systems
• Improved Response Matrix Solution Algorithms
• Even-odd coupled parity equation methods
• Adaptive grid solution algorithms
• Effective parallelization methods