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/Number | Semester/Term Offered | Enrollment |
---|---|---|

NE 591 | Fall 2011 | 9 |

NE 591 | Fall 2012 | 5 |

NE 591 | Spring 2016 | 7 |

Course Delivery

Face-to-Face (On Campus)

Distance Education (DELTA)

Distance Education (DELTA)

Grading Method

Graded/Audit

3

15

Contact Hours

(Per Week)

(Per Week)

Component Type | Contact Hours |
---|---|

Lecture | 3 |

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 Component | Per Semester | Per Section | Multiple Sections? | Comments |
---|---|---|---|---|

Lecture | 7 | 7 | No | Based on this year's enrolment |

Delivery Format | Per Semester | Per Section | Multiple Sections? | Comments |
---|---|---|---|---|

LEC | 3 | 3 | No | based 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

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

Obj. 1) Engage the human experience through the interpretation of culture.

Obj. 2): Become aware of the act of interpretation itself as a critical form of knowing in the humanities.

Obj. 3) Make academic arguments about the human experience using reasons and evidence for supporting those reasons that are appropriate to the humanities.

Each course in the Mathematial Sciences category
of the General Education Program will provide instruction and
guidance that help students to:

Obj. 1) Improve and refine mathematical problem-solving abilities.

Obj. 2) Develop logical reasoning skills.

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

Obj.O 1) Use the methods and processes of science in testing hypotheses, solving problems and making decisions

Obj. 2) Make inferences from and articulate, scientific concepts, principles, laws, and theories, and apply this knowledge to problem solving.

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

Obj. 1) Examine at least one of the following: human behavior, culture, mental processes, organizational processes, or institutional processes.

Obj. 2) Demonstrate how social scientific methods may be applied to the study of human behavior, culture, mental processes, organizational processes, or institutional processes.

Obj. 3) Use theories or concepts of the social sciences to analyze and explain theoretical and or real-world problems, including the underlying origins of such problems.

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

Obj. 1) Distinguish between the distinct approaches of two or more disciplines.

Obj. 2) Identify and apply authentic connections between two or more disciplines.

Obj. 3) Explore and synthesize the approaches or views of two or more disciplines.

1. Which disciplines will be synthesized, connected, and/or considered in this course?

Each course in the Visual and Performing Arts category of the General Education Program will provide instruction and guidance that help students to:

Obj. 1) Deepen their understanding of aesthetic, cultural, and historical dimensions of artistic traditions.

Obj. 2) Strengthen their ability to interpret and make critical judgements about the arts through the analysis of structure, form, and style of specific works.

Obj. 3) Strengthen their ability to create, recreate, or evaluate art based upon techniques and standards appropriate to the genre.

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

Obj. 1) Acquire the fundamentals of health-related fitness, encompassing cardio-respiratory and cardiovascular endurance, muscular strength and endurance, muscular flexibility and body composition.

Obj. 2) Apply knowledge of the fundamentals of health-related fitness toward developing, maintaining, and sustaining an active and healthy lifestyle.

Obj. 3) Acquire or enhance the basic motor skills and skill-related competencies, concepts, and strategies used in physical activities and sport.

Obj. 4) Gain a thorough working knowledge, appreciation, and understanding of the spirit and rules, history, safety, and etiquette of physical activities and sport.

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:

Obj. 1) Identify and examine distinguishing characteristics, including ideas, values, images, cultural artifacts, economic structures, technological or scientific developments, and/or attitudes of people in a society or culture outside the United States.

Obj. 2) Compare these distinguishing characteristics between the non-U.S. society and at least one other society.

Obj. 3) Explain how these distinguishing characteristics relate to their cultural and/or historical contexts in the non-U.S. society.

Obj. 4) Explain how these disinguishing characteristics change in response to internal and external pressures on the non-U.S. society.

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:

Obj. 1) Analyze how religious, gender, ethnic, racial, class, sexual orientation, disability, and/or age identities are shaped by cultural and societal influences.

Obj. 2) Categorize and compare historical, social, political, and/or economic processes producing diversity, equality, and structured inequalities in the U.S.

Obj. 3) Interpret and evaluate social actions by religious, gender, ethnic, racial, class, sexual orientation, disability, and/or age groups affecting equality and social justice in the U.S.

Obj. 4) Examine interactions between people from different religious, gender, ethnic, racial, class, sexual orientation, disability, and/or age groups in the U.S.

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)

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 Method | Weighting/Points for Each | Details |
---|---|---|

Quizzes | 20% | 10 True/False or Multiple Choice questions in beginning of class, 4 times per semester |

Homework | 20% | 4 problems per set, 4 times per semester |

Other | 20% | 4 programming assignments per semester building up to a code that solves the one-speed, steady state radiation transport equation in x,y geometry |

Midterm | 20% | 5 problems, take home |

Final Exam | 20% | 3 or 4 problems take home |

Topic | Time Devoted to Each Topic | Activity |
---|---|---|

Nonlinear Boltzmann equation & linearization to neutron transport equation | 5 lectures | Derivation 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 theory | 4 lectures | Basic 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 equation | 1/2 lecture | NTE numerical meth: A taxonomy |

Energy discretization: Multigroup approximation | 1/2 lecture | Discretization of Energy in NTE: Multigroup (MG) Theory & MG consts |

Angle discretization: Discrete Ordinates | 1 lecture | Discretization of Angle in NTE: Method of Discrete Ordinates (SN) in slab, & multidimensional |

Spatial discretization | 2 lectures | Discretization 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 source | 5 lectures | Iterations: 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 refinement | 8 lectures | Adjoint 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 & acceleration | 1 lecture | Spectral analysis of iterations; Eigenmode convergence |

Advanced topics | 2 lectures | Ray 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

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

ABGS Reviewer Comments:

-None

Key: 10396