ESFR-SMART course on deterministic modelling of nuclear systems

Chalmers Course

Mark your calendar for the “Deterministic modelling of nuclear systems” course organised in the framework of the ESFR-SMART project, in Gothenburg (Sweden), from 9-13 September 2019!

This 5-day course is dedicated to topics covering neutron transport, fluid dynamics and heat transfer. It can be followed either in-person classes or fully online and aims at presenting the main algorithms in the computer codes used by the industry and in academia for the macroscopic modelling of nuclear systems. The underlying methods used in such codes – together with their assumptions and limitations-, will be thoroughly presented, so that codes could be used with confidence. During the course, attendees will also have to develop a one-dimensional coupled model of a heterogeneous sodium-cooled reactor using the presented methods.

Learning objectives

Once completing the course, attendees should be able to:

  • know the governing equations describing neutron transport, flow transport, and heat transfer in nuclear reactors
  • know the modelling strategies used for neutron transport, flow transport, heat transfer in nuclear reactors, and for their coupling
  • understand the limitations of the different modelling strategies

Target audiences

  • MSc & PhD students having some background knowledge in nuclear engineering
  • nuclear engineers
  • reactor physicists
  • nuclear safety analysts


  1. Some basic knowledge in programming is of course a definite advantage for solving the different tasks in case students want to obtain the course credit points. All the computing tasks will be solved using MATLAB. In case students do not already have access to MATLAB, a 30 day-free trial version of MATLAB will be provided.
  2. Although previous knowledge in reactor physics, thermal-hydraulics or nuclear engineering is definitely advantageous: all equations are derived from first principles and should allow students not familiar with reactor modelling to fully understand all concepts.

Teaching approach

This course follows a “flipped classroom” set-up in a hybrid (i.e. on-site/off-site) environment. Students learn asynchronously from lectures and materials made available on the web prior to attending synchronous sessions (either in the classroom for the on-site students or remotely for the off-site students). Such sessions are held in an interactive teaching room in Chalmers University of Technology. The room allows mixing on-site students with remote attendees, while preserving full interaction possibilities between both audiences. Because students learn at their own pace during the asynchronous sessions, they attend the synchronous sessions better prepared. As a result, these sessions can focus on more active forms of learning that effectively engage students, promote higher-order thinking, clarify difficult concepts and provide more personalised support.

Course format

  • pre-recorded lectures or webcasts available to students for on-demand viewing (asynchronous sessions)
  • online quizzes embedded in the webcasts and focusing on conceptual understanding (asynchronous sessions)
  • interactive wrap-up sessions designed to summarise the key concepts presented in the webcasts and to address student needs (synchronous sessions)
  • interactive tutorials during which attendees will have to develop, under the teacher’s supervision and guidance, a one-dimensional coupled model of a heterogeneous sodium-cooled reactor (synchronous sessions)

For the off-site attendees, the interactive wrap-up sessions and tutorials are live-broadcasted on the web.

The course is offered in two set-ups:

  • On-site attendance (limited to 20 participants)
  • Off-site attendance (limited 10 participants)

Course credits

The course is worth 1.5 ECTS. A course certificate will be issued for the students attending all wrap-up/tutorial sessions and being engaged in such sessions.

For the wrap-up sessions, engagement is assessed via participation to the group discussions. For the tutorials, engagement is assessed via solving the given problems.


A handbook specifically written for the course and the corresponding lecture slides will be provided to the students.

Course contents

The curriculum for the course is organised in six chapters.

  1. In the first introductory chapter, the governing equations for neutron transport, fluid transport, and heat transfer are derived, so that students not familiar with any of these fields can understand the course without difficulty. The peculiarities of nuclear reactor systems -i.e. their multi-physic and multi-scale aspects-, are dealt with. An overview of the modelling strategies is thereafter given with particular emphasis on deterministic methods which represents the focus area of the course.
  2. In the second chapter, the computational methods for neutron transport at both the pin cell and fuel assembly levels are presented. The chapter is aimed at following the solution procedure in fuel pin/lattice codes as much as possible. This includes resonance calculations of the cross-sections, the determination of the micro-region micro-fluxes, and of the macro-region macro-fluxes, and finally spectrum correction. The chapter ends with the preparation of the macroscopic cross-sections for subsequent core calculations, where the effect of burnup is also detailed.
  3. In the third chapter, the computational methods in use for core calculations are presented. In the first part of this chapter, the treatment of the angular dependence of the neutron flux is described. In the second part, the treatment of the spatial dependence of the neutron flux is outlined. Thereafter, the solution procedure for estimating the core-wise position (and possibly direction) dependent multigroup neutron flux is described. Finally, the methodology used for determining the core-wise space and time-dependent neutron flux in case of transient calculations is derived.
  4. The fourth chapter focuses on the computational methods used for one/two-phase flow transport and heat transfer. From the local governing equations of fluid flow and heat transfer, macroscopic governing equations are derived and the underlying assumptions clearly emphasised. The different flow models commonly used in nuclear engineering are introduced, models having various levels of sophistication: the two-fluid model, the mixture models with thermal equilibrium and specified drift, and the Homogeneous Equilibrium Model. The temporal and spatial discretisation of the flow and heat transfer models are given special attention, with emphasis on their stability, consistence, and convergence.
  5. The fifth chapter tackles solving the coupling between neutronics and thermal-hydraulics at the core level. Various aspects of multi-physics coupling are highlighted: segregated versus monolithic approaches, coupling terms and nonlinearities, information transfer, preparation of macroscopic material data (cross-sections, diffusion coefficients, and discontinuity factors) as functions of the thermal-hydraulic variables, spatial coupling. The numerical techniques that can be used to solve multi-physics temporal coupling either in a segregated or in a monolithic manner are also discussed in detail.
  6. The last and sixth chapter summarises the macroscopic modelling techniques and presents a quick overview of the current efforts in high-fidelity reactor modelling.


Registration is closed.

Location & venue details

Chalmers University of Technology

Gothenburg (Sweden)

The course starts at 13:00 on September 9th and ends at 14:00 on September 13th.


Christophe Demazière: