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Lecture

Multigroup Theory: Main Equations and Numerical Solution

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 derivation of multi-group diffusion equations, the concept of neutron balance, and the numerical methods for solving the neutron diffusion equation. It explains the group structures, group constants, and the k-eigenvalue problem, emphasizing the importance of accurate group constants for reactor calculations.

Instructors (3)

Mathieu Hursin

Carlo Fiorina

Andreas Pautz

Official source

Ontological neighbourhood

Energy engineering

Nuclear power: Topics in nuclear power

Mathematics

Analysis: Numerical analysis

Related concepts (32)

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.

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.

Numerical methods for partial differential equations

Numerical methods for partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs). In principle, specialized methods for hyperbolic, parabolic or elliptic partial differential equations exist. Finite difference method In this method, functions are represented by their values at certain grid points and derivatives are approximated through differences in these values.

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.

Molten salt reactor

A molten salt reactor (MSR) is a class of nuclear fission reactor in which the primary nuclear reactor coolant and/or the fuel is a mixture of molten salt with a fissionable material. Two research MSRs operated in the United States in the mid-20th century. The 1950s Aircraft Reactor Experiment (ARE) was primarily motivated by the technology's compact size, while the 1960s Molten-Salt Reactor Experiment (MSRE) aimed to demonstrate a nuclear power plant using a thorium fuel cycle in a breeder reactor.

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Covers numerical methods for solving the neutron diffusion equation and addressing heterogeneous effects in thermal reactors.

Multigroup Theory: K-eigenvalue Problem and Numerical Solutions

Explores the practical approach of homogenizing reactor core analysis and the calculation route for multigroup diffusion equations.

Reactor Technology: Reactivity Variations and Control

Explores reactivity variations in reactor technology, covering short-term, medium-term, and long-term effects, means of control, and consequences.

Reactor Kinetics: Point Kinetics Equations