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Viewing: NE 523 : Computational Transport Theory

Last approved: Tue, 30 Aug 2016 14:56:45 GMT

Last edit: Tue, 30 Aug 2016 14:56:45 GMT

Catalog Pages referencing this course
Change Type
Major
NE (Nuclear Engineering)
523
016215
Dual-Level Course
No
Cross-listed Course
No
Computational Transport Theory
Computational Transport
College of Engineering
Nuclear Engineering (14NE)
Term Offering
Spring Only
Offered Every Year
Spring 2017
Previously taught as Special Topics?
Yes
3
 
Course Prefix/NumberSemester/Term OfferedEnrollment
NE 591Fall 20119
NE 591Fall 20125
NE 591Spring 20167
Course Delivery
Face-to-Face (On Campus)
Distance Education (DELTA)

Grading Method
Graded/Audit
3
15
Contact Hours
(Per Week)
Component TypeContact Hours
Lecture3
Course Attribute(s)


If your course includes any of the following competencies, check all that apply.
University Competencies

Course Is Repeatable for Credit
No
 
 
Yousry Y. Azmy
Professor of Nuclear Engineering
Full

Open when course_delivery = campus OR course_delivery = blended OR course_delivery = flip
Enrollment ComponentPer SemesterPer SectionMultiple Sections?Comments
Lecture77NoBased on this year's enrolment
Open when course_delivery = distance OR course_delivery = online OR course_delivery = remote
Delivery FormatPer SemesterPer SectionMultiple Sections?Comments
LEC33Nobased on previous year's enrolment
NE 401/501: Reactor Analysis and Design Advanced math & moderate programming skills are necessary. Permissible programming languages: Fortran or C++
Is the course required or an elective for a Curriculum?
No
Derivation of the nonlinear Boltzmann equation for a rarefied gas and linearization to the equation of transport of neutral particles. Deterministic methods for solving the neutron transport equation: Multigroup energy discretization; Discrete Ordinates angular discretization; various spatial discretization methods. Convergence of numerical solutions with discretization refinement. Iterative solution algorithms: inner, outer, and power iterations. Spectral analysis of inner iterations convergence and acceleration. Selection of advanced topics.

This course will introduce first year graduate students and advanced seniors in the Department of Nuclear Engineering to a broad selection of computational topics in radiation transport. Advanced mathematical analysis techniques that serve computational methods' purposes are covered then deployed to illustrate their utility in the design and analysis of numerical methods and solution algorithms. Homework assignments require the students to implement some of the covered methods and algorithms in a sequence of computer codes using Fortran or C++ as these are the most common programming languages for computationally intensive applications like radiation transport.


No

Is this a GEP Course?
GEP Categories

Humanities Open when gep_category = HUM
Each course in the Humanities category of the General Education Program will provide instruction and guidance that help students to:
 
 

 
 

 
 

 
 

 
 

 
 

Mathematical Sciences Open when gep_category = MATH
Each course in the Mathematial Sciences category of the General Education Program will provide instruction and guidance that help students to:
 
 

 
 

 
 

 
 

Natural Sciences Open when gep_category = NATSCI
Each course in the Natural Sciences category of the General Education Program will provide instruction and guidance that help students to:
 
 

 
 

 
 

 
 

Social Sciences Open when gep_category = SOCSCI
Each course in the Social Sciences category of the General Education Program will provide instruction and guidance that help students to:
 
 

 
 

 
 

 
 

 
 

 
 

Interdisciplinary Perspectives Open when gep_category = INTERDISC
Each course in the Interdisciplinary Perspectives category of the General Education Program will provide instruction and guidance that help students to:
 
 

 
 

 
 

 
 

 
 

 
 

 
 

 
 

Visual & Performing Arts Open when gep_category = VPA
Each course in the Visual and Performing Arts category of the General Education Program will provide instruction and guidance that help students to:
 
 

 
 

 
 

 
 

 
 

 
 

Health and Exercise Studies Open when gep_category = HES
Each course in the Health and Exercise Studies category of the General Education Program will provide instruction and guidance that help students to:
 
 

 
 

 
 

 
 

 
&
 

 
 

 
 

 
 

Global Knowledge Open when gep_category = GLOBAL
Each course in the Global Knowledge category of the General Education Program will provide instruction and guidance that help students to achieve objective #1 plus at least one of objectives 2, 3, and 4:
 
 

 
 

 
Please complete at least 1 of the following student objectives.
 

 
 

 
 

 
 

 
 

 
 

US Diversity Open when gep_category = USDIV
Each course in the US Diversity category of the General Education Program will provide instruction and guidance that help students to achieve at least 2 of the following objectives:
Please complete at least 2 of the following student objectives.
 
 

 
 

 
 

 
 

 
 

 
 

 
 

 
 

Requisites and Scheduling
 
a. If seats are restricted, describe the restrictions being applied.
 

 
b. Is this restriction listed in the course catalog description for the course?
 

 
List all course pre-requisites, co-requisites, and restrictive statements (ex: Jr standing; Chemistry majors only). If none, state none.
 

 
List any discipline specific background or skills that a student is expected to have prior to taking this course. If none, state none. (ex: ability to analyze historical text; prepare a lesson plan)
 

Additional Information
Complete the following 3 questions or attach a syllabus that includes this information. If a 400-level or dual level course, a syllabus is required.
 
Title and author of any required text or publications.
 

 
Major topics to be covered and required readings including laboratory and studio topics.
 

 
List any required field trips, out of class activities, and/or guest speakers.
 

No new resources are required. The course will be taught by Dr. Yousry Azmy who is a current faculty in the Department of Nuclear Engineering as part of his annual teaching commitment.

This course seeks to provide the students with:



  • Fundamental understanding of the physics & mathematics underpinnings of neutron transport theory

  • Thorough understanding of the computational challenges in solving the neutron transport equation (NTE)

  • Full coverage of and hands-on experience with numerical methods employed in solving the NTE

  • Exposure to and utilization of basic software engineering practices and debugging strategies


Student Learning Outcomes

By the end of this course the students will be able to:



  • Explain the physics foundation of the neutron transport equation (NTE) and its underlying assumptions

  • Identify relationships among various numerical methods employed in solving the NTE

  • Analyze and justify discretization methods in energy, angle, and space for computationally solving the NTE

  • Apply spectral analysis to predict performance of iterative algorithms for solving the NTE

  • Implement new Fortran or C++ code or maintain existing code for solving the NTE


Evaluation MethodWeighting/Points for EachDetails
Quizzes20%10 True/False or Multiple Choice questions in beginning of class, 4 times per semester
Homework20%4 problems per set, 4 times per semester
Other20%4 programming assignments per semester building up to a code that solves the one-speed, steady state radiation transport equation in x,y geometry
Midterm20%5 problems, take home
Final Exam20%3 or 4 problems take home
TopicTime Devoted to Each TopicActivity
Nonlinear Boltzmann equation & linearization to neutron transport equation5 lecturesDerivation of the Boltzmann equation for one-species rarefied gas followed by generalization to multi-species. Linearization of resulting integro-differential for terrestrial neutronic systems.
Theoretical aspects of transport theory4 lecturesBasic definitions of quantities involved in Transport Theory; NTE Assumptions: Initial & Boundary Conditions; Vector Spaces & Scalar Products; Orthonormal Basis; Scattering Source: Spherical Harmonics
Overview of numerical methods for solving the transport equation1/2 lectureNTE numerical meth: A taxonomy
Energy discretization: Multigroup approximation1/2 lectureDiscretization of Energy in NTE: Multigroup (MG) Theory & MG consts
Angle discretization: Discrete Ordinates1 lectureDiscretization of Angle in NTE: Method of Discrete Ordinates (SN) in slab, & multidimensional
Spatial discretization2 lecturesDiscretization of Spatial dependence in NTE-SN: Diamond Difference (DD), Characteristic, Nodal, Linear-Discontinuous (LD), Discontinuous-Galerkin Finite Element (DGFEM)
Solution algorithms: Mesh sweep; inner/outer iterations; fission/scattering source5 lecturesIterations: multidimensional mesh sweep & Inner iterations; Integral Form of TE with isotropic & anisotropic scattering; Criticality: Steady-state solution; k-ev; k- vs alpha-eigenproblem; Iterations: Outer; Power
Convergence of numerical solutions with discretization refinement8 lecturesAdjoint basics; Adjoint non-multiplying TE; importance. Existence & uniqueness of TE solution
Invariance & symmetry: Dimension & size reduction
Asymptotics; Numerical solution convergence.
Convergence of TE numerical solutions: E, Omega, r.
SN solution: existence, regularity, uniqueness, non-negativity, convergence. Error analysis of Diamond Difference method in 2D
Iterative convergence & acceleration1 lectureSpectral analysis of iterations; Eigenmode convergence
Advanced topics2 lecturesRay effects; bootstrapping; multiprocessing
mlnosbis 5/20/2016: No overlapping courses. Is consultation needed?

ghodge 5/31/2016 No consultation need. Ready for ABGS reviewers.

ABGS Reviewer Comments:
-None
Key: 10396