NE 255 - Numerical Simulation in Radiation Transport
Fall 2008
Prof. Jasmina Vujic
(vujic@maxwell.berkeley.edu)
TuTh 11:00 - 12:30 am, 237 Cory Hall
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NE 255 - Numerical Simulation in Radiation Transport
Fall 2008
Prof. Jasmina Vujic
(vujic@maxwell.berkeley.edu)
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 28 |
Introduction. Organization. Overview of Computational Science/Engineering. A Brief History of Computer Technology and Architecture. | Handouts 1 |
| II/2 | Sep 2 |
Types of equations in radiation transport. General types of differential and integral equations. Integro-differential form of transport equation. Integral form of transport equation. Definitions of neutron number density, neutron flux and current. | Handouts 2 |
| II/3 | Sep 4 |
Derivation of neutron transport
equation
in integro-differential form. Initial and Boundary Conditions.
Simplified forms of neutron transport equation. |
Handouts 3 |
| III/4 | Sep 9 |
Review of Numerical Simulations: Deterministic and Probabilistic Methods. Numerical solution of neutron transport/diffusion equation - discretization in time, energy, angle and space. | Handouts 4 |
| III/5 | Sep 11 | Introduction to the MCNP code. MCNP input and
output description. Simple Monte Carlo problems. Examples. (Max Fratoni) |
Handouts 5 MCNP Input Manual |
| IV/6 |
Sep 16 |
Ranning MCNP in
parallel
mode. Introduction to MOCUP: The time
dependent Monte Carlo
calculationsDiscussion about
MCNP/MOCUP results. (Max Fratoni) |
Handouts 6 |
| IV/7 |
Sep 18 |
Adjoint transport equation and
its aplications. (Ehud Greenspan) |
Handouts
7 |
| V/8 | Sep 23 |
Neutron Transport Equation in 1D: Numerical Solution of Integro-Differential Equation. Spatial discretization in slab geometry: diamond-difference, step-difference, step characteristic methods. | Handouts 8 HW 1 due |
| V/9 | Sep 25 | Angular discretization: Discrete-ordinates (Sn) method. Some Sn Gauss-Legendre quadrature sets. Solution of fixed-source problems with and without scattering | Handouts 9 |
| VI/10 | Sep 30 |
Iterative methods for solving discretized equations. Source iteration for k-eigenvalue problems. Convergence of source iteration method. Multigroup Sn problems. | Handouts 10 |
| VI/11 | Oct 2 |
Multidimensional discrete ordinates (Sn) methods
(angular quadrants, ray effects, streaming effects). Multigroup
discrete ordinates method. Discrete-ordinates computer codes. Angular discretization: Pn method. |
Handouts 11 HW 2 due |
| VII/12 | Oct 7 |
Dearivation of Neutron Diffusion Equation in 3D.
Neutron Diffusion Equation in 1D: Numerical
Solution of the 2nd Order ODE. |
Handouts 12 |
| VII/13 | Oct 9 |
Neutron Diffusion Equation in 1D: Formulation of
the finite difference
equations for the "fixed source" problem. Direct
solution by Gaussian elimination.
Iterative solutions by Jacobi, Gauss-Seidel and SOR Methods.
Formulation of the finite difference equation
for the "eigenvalue
(criticality)" problem. (Mathieu Hursin) |
Handouts 14 HW 3 due |
| VIII/14 | Oct 14 | MIDTERM (Mathieu Hursin) |
|
| VIII/15 | Oct 16 | Power and "inverse" power iterative method. Krylov methods for iterative solution of linear systems. (Mathieu Hursin) | Handouts 15 |
| IX/16 | Oct 21 |
Formulation of the finite difference
equations in 2D. Formulation of finite element equations in 1D. |
Handouts 16 Handouts 16a |
| IX/17 | Oct 23 |
Preliminari Project Presentations (5-10 min) | |
| X/18 | Oct 28 |
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 18 |
| X/19 | Oct 30 |
Examples of sampling from a given
distributions. Monte Carlo simulation of neutron transport. Sampling of the position, direction, distance to collision, typeo of collision,... |
Handouts 19 RNUM HW 4 due |
| XI/20 | Nov 4 |
Complex
geometry description and ray tracing. Error estimates. All-particle Monte Carlo simulation. Vector and parallel Monte Carlo simulations. |
Handouts 20 MC-Parallel |
| XI/21 | Nov 6 |
Monte Carlo simulation of neutron transport.
Sampling of the position, direction, distance to collision, typeo of
collision,...Sampling of energy and angle in Compton scattering. Definitions of true and sample mean, variance, standard deviation. Central limit theorem. Collision and tracklenght estimators for flux calculation. |
Handouts 21 Compton Scattering |
| XII | Nov 11 |
Veterans Day Holiday |
|
| XII/22 | Nov 13 |
Derivation of Method of Characteristics in two dimensions. Choice of angles. Choice of Boundary Conditions. (Mathieu Hursin) | Handouts 22 |
| XIII/23 | Nov 18 |
Derivation of neutron transport equation in integral form. Derivation of adjoint transport equation. | Handouts 23 |
| XIII/24 | Nov 20 |
Method of Characteristics in three dimensions.
MOC codes. Approximation
methods for solving 3D MOC problems. Applications of the DeCART MOC
code. (Mathieu Hursin) |
Handouts 24 |
| XIV/25 | Nov 25 |
Solving integral form of neutron transport equation. Collision probality method. Derivation of collision probability equations in 2D and 3D. | Handouts 22 Handouts 25 HW 5 due |
| XV/26 | Dec 2 |
Diffusion theory codes. Application of PARCS to the LWRs and HTRs. (Mathieu Hursin) | Handouts 26 |
| XV/27 | Dec 4 |
Project presentations |
|
| XVI/28 | Dec 9 |
Project presentations | |
| Dec 10 |
Extra Homework due |