Lecture

Multigroup Theory: Main Equations and Numerical Solution

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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)

Andreas Pautz

Teaching & PhD PhD Students Sofia Portolan, Michel Saliba, Bishal Torrente, Alexis Paul Boris Claude Dupont-Bembinoff, Cynthia Camila Güttlein Past EPFL PhD Students Ting Zhu, Vladimir Vladimirov Brankov, Boris Aviv Hombourger, Damar Canggih Wicaksono, Petra Mala, Adolfo Rais, Valentyn Bykov, Daniel Jerôme Siefman, Evgeny Nikitin, Dionysios Chionis, Oskari Ville Pakari, Friederike Bostelmann, Jiani Gao, Efstathios Vlassopoulos, Alessandro Scolaro, Stefan Radman, Alexander Aures, Lubomír Bures, Ahmed Salah

Mathieu Hursin

Current work I'm currently heavily involved in the nuclear data community and with technical work towards the improvement of the latest version of the European library (JEFF). I'm leading an OECD/NEA subgroup in that direction. I'm also leading a Euratom project towards the production of multi-physics experimental data suitable for the validation of high-fidelity, high-resolution simulation tools. After a doctoral thesis on the high-fidelity modeling of control rod ejection in a pressurized water reactor at

Carlo Fiorina

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.

Boiling water reactor

A boiling water reactor (BWR) is a type of light water nuclear reactor used for the generation of electrical power. It is the second most common type of electricity-generating nuclear reactor after the pressurized water reactor (PWR), which is also a type of light water nuclear reactor. The main difference between a BWR and PWR is that in a BWR, the reactor core heats water, which turns to steam and then drives a steam turbine. In a PWR, the reactor core heats water, which does not boil.

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.

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