NE 255 - Numerical Simulation in Radiation Transport
Fall 2006 - Lectures, Prof. Jasmina Vujic and Prof. Thomas Downar
TuTh 11:00 - 12:30 am, 237 Cory Hall
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NE 255 - Numerical Simulation in Radiation Transport
Fall 2006 - Lectures, Prof. Jasmina Vujic and Prof. Thomas Downar
TuTh 11:00 - 12:30 am, 237 Cory Hall
Back to NE 255
Home
page
| Week/ Lecture |
date | Topic | Chapter in Textbook |
| I/1 | Aug 29 |
Introduction. Organization. Overview & Goals. Renaissance
of Nuclear Energy Option. |
Course Description On-Line Reources Handouts 1 |
| I/2 | Aug 31 |
Overview of Computational Science/Engineering. A Brief History of Computer Technology and Architecture. | Handouts 2 |
| II/3 | Sep 5 |
Types of equations in radiation transport. General
types of differential
and integral equations. Integro-differential form of transport
equation.
Integral form of transport equation. Derivation of neutron transport
equation
in integro-differential form. |
Handouts 3 |
| II/4 | Sep 7 |
Derivation of neutron transport equation in integral form.
Derivation
of adjoint equation. Neutron diffusion equation. Review of Numerical
Simulations:
Deterministic and Probabilistic Methods |
Handouts 4 |
| III/5 | Sep 12 | Numerical solution of neutron transport/diffusion equation - discretization in time, energy, angle and space. | Handouts 5 |
| III/6 | Sep 14 | Neutron Transport Equation in 1D: Numerical Solution of Integro-Differential Equation. Spatial discretization in slab geometry: diamond-difference, step-difference, step characteristic methods. | |
| IV/7 | Sep 19 |
Angular discretization: Discrete-ordinates (Sn) method. Some Sn Gauss-Legendre quadrature sets. Solution of fixed-source problems with and without scattering | |
| IV/8 | Sep 21 |
Iterative methods for solving discretized equations. Source iteration for k-eigenvalue problems. Convergence of source iteration method. Multigroup Sn problems. | |
| V/9 | Sep 26 | Multidimensional discrete ordinates (Sn) methods
(angular quadrants, ray effects, streaming effects). Multigroup
discrete ordinates method. Discrete-ordinates computer codes. Angular discretization: Pn method. |
|
| V/10 | Sep 28 |
MIDTERM I |
|
| VI/11 | Oct 3 |
Solving integral form of neutron transport
equation. Collision
probality method. Derivation of collision probability equations in 2D
and
3D. |
Handouts 11 |
| VI/12 | Oct 5 |
Ray tracing in general 3D geometries. Optimization for vector and parallel processing. | |
| VII/13 | Oct 10 | Neutron Diffusion Equation in 1D: Numerical
Solution of the 2nd Order ODE. Formulation of the finite difference
equations for the "fixed source" problem. |
Handouts 13 |
| VII/14 | Oct 12 | Direct solution by Gaussian elimination.
Iterative solutions by Jacobi, Gauss-Seidel and SOR Methods. |
Handouts 13 Preliminary reports due |
| VIII/15 | Oct 17 | Introduction to the MCNP code. Raning MCNP in parallel mode. | Max Fratoni MCNP Slides |
| VIII/16 | Oct 19 Tom Downar |
Krylov methods for iterative solution of linear systems. Formulation of the finite difference equation for the "eigenvalue (criticality)" problem. Power and "inverse" power iterative method. | Handouts 16 Handouts 16a |
| IX/17 | Oct 24 Tom Downar |
Numerical Solution of the 2nd Order ODE. by Finite-element method. Nodal methods. Diffusion equation in two or more dimension. | Handouts 17 Handouts 17a |
| IX/18 | Oct 26 Tom Downar |
Diffusion theory codes. Application of PARCS to
the LWRs and HTRs. |
|
| X/19 | Oct 31 |
MIDTERM II | |
| X/20 | Nov 2 |
Monte Carlo Method: Continuous and discrete
probability distribution. Probability density function.
Cumulative probability distribution
function. Random numbers. Categories of random sampling. Analog Monte Carlo. Nonanalog Monte Carlo. Importance sampling. Variance reduction methods. |
Handouts 20 |
| XI/21 | Nov 7 |
Method of Characteristics in two dimensions.
Choice of Angles. Choice of boundary conditions. |
|
| XI/22 | Nov 9 |
Ray tracing in general geometry. Linearly anisotropic
scattering. |
|
| XII/23 | Nov 14 Tom Downar |
MOC in three dimensions. MOC codes. Approximate
methods for solving 3D MOC problems. Applications w/ the DeCART MOC
code. |
|
| XII/24 | Nov 16 Tom Downar |
Coupled Field Solutions: Numerical
Considerations |
|
| XIII/25 | Nov 21 Tom Downar |
Coupled Field SOlutions: Applications - Coupled
MOC/CDF. Coupled Monte Carlo/CDF |
|
| XIV/26 | Nov 28 |
Complex geometry description and ray tracing. Monte Carlo simulation of neutron and photon transport. Error estimates. | |
| XIV/27 | Nov 30 |
All-particle Monte Carlo simulation. Vector and parallel Monte Carlo simulations. |
|
| XV/28 | Dec 5 |
MOCUP: The time dependent Monte Carlo calculations. | Handouts Max Fratoni Reports due |
| XV/29 | Dec 7 |
Project presentations | Reports |