Neutron Transport With Finite Differences

Using C++

What you'll learn

Learn what the neutron diffusion equation is about and how that affects nuclear reactor power and behaviour.

Discretize the neutron diffusion equation in 1, 2 and 3 dimensions using the finite differences.

Learn how to program in C++ language a finite difference solver of the diffusion equation.

Understand the multi-energy group participation terms in the neutron equation.

Learn how to handle sparse matrices and how to solve linear system of equations iteratively under specific conditions.

Solve neutron diffusion with sources (linear system) or calculate the criticity factor (eigenvalue problem)

Requirements

Some programming experience is welcome since we are going to use some C++ containers, but in the end I explain and justify absolutely everything so it shouldn't be very hard to follow the course.

Description

You are a nuclear, or a software engineer, maybe a physicist, or a nerd. This course caught your attention, would you like why? Because it is extremelly rare to find an online course on this topic. The course exposes what typical nuclear engineering students learn in a full study of nuclear engineering. There are universities where this topic is even not covered and student limit themselves to simple analytical solutions for the engineering problems or they end relying on existing private software to get results. If you are curious and you want to learn how to model nuclear reactors and compute the criticallity factor of one of them, you may want to look into the course.This course is for those who want to learn how to solve the neutron diffusion equation in 1D, 2D and 3D using finite differences and how to model a nuclear reactor core. We use sparse matrices and the conjugate gradient method in C++ to achieve this goal. The course covers theory, coding practice and has exercises that help to improve the knowledge and retention of what we learn. We also face the multi-group theory for improving the precision in the computations of the criticality factor. On different parts of the course we validate that the software gives the right solution using analytical results from the literature.

Overview

Section 1: Introduction

Lecture 1 Discretization 1D

Lecture 2 Coding session: diffusion in 1D with neutron source (part a)

Lecture 3 Coding session: diffusion in 1D with neutron source (part b)

Lecture 4 Algorithm to compute the criticity factor Keff

Lecture 5 Coding session: diffusion in 1D with Keff (part a)

Lecture 6 Coding session: diffusion in 1D with Keff (part b)

Lecture 7 Coding session: validation of diffusion in 1D with Keff

Lecture 8 Control Rods Simulation

Section 2: Diffusion in 2D and 3D

Lecture 9 Discretization in 2D

Lecture 10 Coding Session: Diffusion in 2D with Keff

Lecture 11 Coding Session: Diffusion in 2D with Keff, solution visualization

Lecture 12 Coding Session: Diffusion in 2D with Keff, validation

Lecture 13 Discretization in 3D

Lecture 14 Coding Session: Diffusion in 3D with Keff

Lecture 15 Coding Session: Diffusion in 3D with Keff, solution visualization

Lecture 16 Coding Session: Diffusion in 3D with Keff, validation

People that wants to understand about nuclear reactor simulations or numerical modeling.,People that have a combined love between physics and computer science.,People who want to give a good use to computers.,Nerds in general.