Monte Carlo Analysis
Monte Carlo is often the method of choice to solve complex problems
in nuclear criticality safety and radiation shielding. To use Monte
Carlo effectively, the analyst must understand the theoretical and computational
fundamentals of the method, as well as the computational options available
in particular computer tools. Also, it is sometimes advantageous
to create new special-purpose Monte Carlo programs to solve particular
problems rather than use an existing program. With these facts in
mind, this course has the following objectives:
-
To familiarize the student with the basic concepts of the Monte Carlo method
in a general (non-transport) context to add to the students’ ability to
apply method to a variety of problems in mathematics, physics, and engineering.
-
To familiarize the student with the particular mathematical techniques
and probability distributions that are used in analog Monte Carlo solutions
of neutral-particle radiation transport problems. This is reinforced
through an in-class exercise that develops an analog Monte Carlo code solution
to a simple slab transport problem.
-
To familiarize the student with the mathematical basis for variance reduction
techniques: non-analog mathematical methods that increase the efficiency
of the calculation without biasing the solution. This is reinforced
with a continuation of the in-class exercise to incorporate variance reduction
techniques.
-
To apply the lessons learned to the most commonly used Monte Carlo code,
MCNP. In a series of hands-on exercises with the PC version of MCNP,
the novice user will learn to set up simple problems, and all levels of
users will gain experience in using the variance reduction techniques offered
by the MCNP code.
Special attention will be given to the understanding of the use of adjoint
calculations in transport analyses, both as an alternate means of obtaining
system responses and as importance functions for accelerating Monte Carlo
forward solutions. Advantages and disadvantages of the adjoint mode versus
the forward mode of analysis will be described. In addition, the
relationship of Monte Carlo methods to deterministic methods will be described,
including strategies involving the hybrid use of both methods to more efficiently
solve certain transport problems.
RESOURCE MATERIAL PROVIDED
Lecture notes including a hard copy of all view graphs and web pages
used in the course.
COURSE SCHEDULE
Monday, August 10, 2009
-
History and Fundamental Concepts of Monte Carlo
-
Statistical Uncertainty of Monte Carlo Estimates
-
Choosing random numbers from distributions
Tuesday, August 11, 2009
-
Use of Monte Carlo to Evaluate Integrals
-
Analog Monte Carlo Transport: The Random Walk
-
In-class Development: Two Group Slab Transmission MC Code
-
Heuristic Variance Reduction Techniques
Wednesday, August 12, 2009
-
Splitting and Russian Roulette
-
Importance Function Biasing
-
In-class Development: Modification of MC Code to Incorporate Variance Reduction
Thursday, August 13, 2009
-
Features of the MCNP Computer Code
-
Geometric modeling in MCNP
-
Other MCNP Input Options
-
MCNP Variance Reduction Options
Friday, August 14, 2009
-
Importance and Use of the Adjoint Flux in MCNP
-
Coupled Deterministic/Monte Carlo Analysis
INSTRUCTOR
Dr. R.E. Pevey is an Associate Professor of Nuclear Engineering at the
University of Tennessee. Before joining the faculty in 1995,
he worked fifteen years at the Savannah River Site in the area of transport
theory methods development, reactor design, and radiation shielding analysis.