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Lecture

Multigroup Theory: K-eigenvalue Problem and Numerical Solutions

In course

PHYS-443: Physics of nuclear reactors

In this course, one acquires an understanding of the basic neutronics interactions occurring in a nuclear fission reactor as well as the conditions for establishing and controlling a nuclear chain reaction. ...

Description

This lecture covers the multigroup theory, focusing on the k-eigenvalue problem and providing an example of an infinite slab reactor with a reflector solved numerically. It explains the practical approach of homogenizing reactor core analysis by calculating few-group constants and using them in a multigroup diffusion analysis. The lecture also discusses the energy group structure and the calculation route for the multigroup diffusion equations.

Instructors (3)

Andreas Pautz

Mathieu Hursin

Carlo Fiorina

Official source

Ontological neighbourhood

Energy engineering

Nuclear power: Topics in nuclear power

Mathematics

Analysis: Numerical analysis

Related concepts (32)

Numerical stability

In the mathematical subfield of numerical analysis, numerical stability is a generally desirable property of numerical algorithms. The precise definition of stability depends on the context. One is numerical linear algebra and the other is algorithms for solving ordinary and partial differential equations by discrete approximation. In numerical linear algebra, the principal concern is instabilities caused by proximity to singularities of various kinds, such as very small or nearly colliding eigenvalues.

Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.

Nuclear reactor

A nuclear reactor is a device used to initiate and control a fission nuclear chain reaction or nuclear fusion reactions. Nuclear reactors are used at nuclear power plants for electricity generation and in nuclear marine propulsion. Heat from nuclear fission is passed to a working fluid (water or gas), which in turn runs through steam turbines. These either drive a ship's propellers or turn electrical generators' shafts. Nuclear generated steam in principle can be used for industrial process heat or for district heating.

Neutron temperature

The neutron detection temperature, also called the neutron energy, indicates a free neutron's kinetic energy, usually given in electron volts. The term temperature is used, since hot, thermal and cold neutrons are moderated in a medium with a certain temperature. The neutron energy distribution is then adapted to the Maxwell distribution known for thermal motion. Qualitatively, the higher the temperature, the higher the kinetic energy of the free neutrons. The momentum and wavelength of the neutron are related through the de Broglie relation.

Numerical methods for ordinary differential equations

Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.

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