ReCoDE - Neutron Diffusion Model¶

Description¶

This code is part of the Research Computing and Data Science Examples (ReCoDE) project. The code itself is a 1-dimensional neutron diffusion solver written in Fortran in an object-oriented format. The example will focus on features of the code that can be used as a teaching aid to give readers some experience with the concepts such that they can implement them in the exercises or directly in their own codes. An understanding of neutron diffusion and reactor physics is not required for this example, but a discussion of the theory can be found in the bottom section of this readme.

Learning Outcomes¶

• Compiled Codes and Makefiles
• Compiler Directives
• Object-Oriented Programming
• Reading input data from file
• Generating output files
• Using ParaView to visualise numerical results
• Solving mathematical problems
• Discretisation of a spatial dimension
• Optimised data storage
• Using build tools CMake and fpm
• Incorporating external libraries (PETSc)

Requirements¶

Academic¶

Entry level researcher with basic knowledge of Fortran syntax. For a Fortran crash course see here

System¶

Getting Started¶

You will be needing Anaconda and a shell/bash terminal to run this code. Optionally, you can use Visual Studio Code as your code editor to work on the exemplar.

Creating the Anaconda Environment¶

The first thing required to build the project is to create the Anaconda environment that contains all the necessary tools to run the exemplar. This can be done by running the following command in a terminal:

conda env create -f environment.yml

You have now created a new Anaconda environment. To activate your Anaconda environment run:

conda activate diffusion

All the following steps take place from a terminal that has the diffusion Anaconda environment activated.

Compiling the Code¶

As Fortran is a compiled language, the code must first be compiled before it can be executed. To do so, a convenience script has been included to get you started:

./install.sh

or alternatively

fpm build

This runs a few commands, feel free to peek into the install.sh file to see how the code is compiled, although we will be covering building/compiling in detail in sections 3 - Compilation Basics and 7 - Build Tools. The summary of the script is that it calls cmake which configures your project by checking for dependencies and generating the necessary Makefiles for compilation. It then compiles the project using the generated Makefiles, and then it finally installs the program inside a folder called install/bin.

To run the installed program, run the following command in a terminal:

./install/bin/diffusion

or alternatively

fpm run

This command tells the executable to run and will generate relevant output files containing the solution to the problem.

Input Options¶

The code is designed such that the user can easily change the problem which the code is attempting to solve. The code uses the input file input.in to read details about the problem, such as the positions of boundaries or materials in the problem. An example of such an input can be seen below:

------------------------------------------
Regions: - Integer number of regions in the problem
2
------------------------------------------
Boundaries: - Real number positions of the boundaries between the regions (one per line)
0.0
0.5
1.0
------------------------------------------
Nodes: - Integer number of nodes in each region (one per line)
5
5
------------------------------------------
Materials: - Fuel, Water or Steel (one per line)
Fuel
Fuel
------------------------------------------
Boundary_Conditions: - Zero or Reflective (two parameters - one per line)
Zero
Zero
------------------------------------------

For this example problem, we are stating that we have a geometry ranging from x = 0.0 to 1.0, half fuel and half steel with a central boundary at x = 0.5. As seen from the above input, the code needs four different parameters to be described to it.

Anatomy of input.in¶

• Regions - An integer number of regions that exists within the problem. We have 1 region from 0.0 to 0.5 and another from 0.5 to 1.0, hence we give the code the integer number 2.
• Boundaries - The positions of the boundaries within the problem. Our first boundary is at the start of our geometry, so we enter the number 0.0. We then have an internal boundary halfway through the problem separating the regions, so we enter the number 0.5. Finally, we have the exterior boundary of our geometry, so we enter the number 1.0. The code will always read one more value here than the number of regions in the problem.
• Nodes - This describes how refined we want the geometry in each region. For the example we want a quick solve with just enough nodes to see the flux profile. As we need to describe this for each region we enter the value 10 twice. The code will always read the same number of values here as the number of regions in the problem.
• Materials - This described the materials that are present within the system. The first half of our geometry is fuel, with the latter half being Steel, so we enter Fuel and Steel. The code will always read the same number of values here as the number of regions in the problem.
• Boundary Conditions - This tells the code what boundaries exist at the edges of our problem. Two boundary conditions have been implemented in out code, that of 'Zero' and 'Reflective'. The former simply ensures that the flux will tend to zero at the boundary, while the latter ensures that the derivative of the flux will tend to zero at the boundary.

Reading Output Files¶

The code generates two output files, OutputFile.txt and OutputFile.vtu. The former is a simple text file containing the position and flux of the solution to the problem. These are simply given in two columns such that they can be read easily by something like a GNUPlot or Python script. An example of such a flux profile can be seen below:

0.000000E+00  0.135813E+01
0.166667E+00  0.137306E+01
0.333333E+00  0.141907E+01
0.500000E+00  0.150000E+01
0.666667E+00  0.158093E+01
0.833333E+00  0.162694E+01
0.100000E+01  0.164187E+01

The results can easily then be visualised using Python, Excel, GNUPlot or any other drawing tool.

The OutputFile.vtu file stores additional data such as the region and cell numbers in an XML format. This can be directly read by software such as ParaView, allowing for more interactive visualisations than that of the previous flux profile. For visualisation purposes, the data has been smeared in a second dimension, which should give users an idea of how multidimensional cell data can be viewed. An example output from ParaView can be seen in the image below by running the following command in a terminal:

paraview OutputFile.vtu

Project Structure¶

.
├── app
│   └── main.F90
├── docs
├── environment.yml
├── fpm.toml
├── input.in
├── install
│   ├── bin
│   │   └── diffusion
│   ├── include
│   └── lib
│       ├── libdiffusion.a
│       └── libdiffusion.so
├── install.sh
├── mkdocs.yml
├── README.md
├── solutions
├── src
│   ├── Constants.F90
│   ├── CRS.F90
│   ├── Materials.F90
│   ├── MatGen.F90
│   ├── Matrix_Base.F90
│   ├── Output.F90
│   ├── PETSc
│   │   ├── PETSc_Init.F90
│   │   ├── PETSc_Ksp.F90
│   │   ├── PETSc_Mat.F90
│   │   └── PETSc_Vec.F90
│   ├── PETScSolver.F90
│   ├── Problem.F90
│   └── Solver.F90
└── tools
    ├── fluxplot
    └── plot.py