• 1 Examples by problem type
• 2 Test suite
• 3 Detailed list of examples

The FeenoX examples are divided by the type of problem they solve:

1. Basic mathematics
2. [Systems of ODEs/DAEs]
3. Laplace’s equation
4. Heat conduction
5. Elasticity (small and large def.)
6. Modal analysis
7. Neutron diffusion
8. Neutron $S_N$

Each type of partial differential equation (i.e. from Laplace downward) is implemented in a subdirectory within src/pde of the source tree. Feel free to…

• ask questions in the Github discussion page
• propose features, corrections, improvements, etc.
• create a pull request for other PDEs. Candidates would be
  • fluid mechanics
  • thermal hydraulics
  • electromagnetism
  • non-linear elasticity
  • cell-level neutronics (i.e. method of characteristics, collision probabilities, etc)

All the files needed to run these examples are available in the examples directory of the Git repository and any of the tarballs, both source and binary.

For a presentation of these examples, see the “FeenoX Overview Presentation” (August 2021).

• Recording (audio in Spanish, slides in English)
• Slides in PDF
• Markdown examples sources

The tests directory in the Github repository has dozens of test cases which can be used as examples for reference and for mathematical verification of the results obtained with FeenoX. These are run when doing make check after compiling the source code.

The test cases usually return a single number (which should be near zero) comparing the numerical result with the expected one. Feel free to propose benchmark problems to add to the suite.

• Basic mathematics
  • Hello World (and Universe)!
  • Ten ways of computing π
  • Financial decisions under inflation
  • The logistic map
  • The Fibonacci sequence
    • Using the closed-form formula as a function
    • Using a vector
    • Solving an iterative problem
  • Computing the derivative of a function as a Unix filter
  • On the evaluation of thermal expansion coefficients
  • Buffon’s needle
• Ordinary Differential Equations & Differential-Algebraic Equations
  • Lorenz’ attractor—the one with the butterfly
  • The double pendulum
  • Vertical boiling channel
    • Original Clausse-Lahey formulation with uniform power distribution
    • Arbitrary power distribution
  • Reactor point kinetics
    • Cinética puntual directa con reactividad vs. tiempo
    • Cinética inversa
    • Control de inestabilidades de xenón
    • Mapas de diseño
• Laplace’s equation
  • How to solve a maze without AI
    • Transient top-down
    • Transient bottom-up
  • Potential flow around an airfoil profile
• Heat conduction
  • Thermal slabs
    • One-dimensional linear
  • Transient heat conduction from steady-state by “turning off” BCs
  • Non-dimensional transient heat conduction on a cylinder
  • Non-dimensional transient heat conduction with time-dependent properties
• Elasticity (small and large deformation)
  • NAFEMS LE10 “Thick plate pressure” benchmark
  • NAFEMS LE11 “Solid Cylinder/Taper/Sphere-Temperature” benchmark
  • NAFEMS LE1 “Elliptical membrane” plane-stress benchmark
  • Parametric study on a cantilevered beam
  • Parallelepiped whose Young’s modulus is a function of the temperature
    • Thermal problem
    • Mechanical problem
  • Orthotropic free expansion of a cube
  • Thermo-elastic expansion of finite cylinders
  • Temperature-dependent material properties
  • Two cubes compressing each other
  • Steel/aluminum paradox
  • NAFEMS GNL5 “Large-deformation beam”
• Mechanical modal analysis
  • Optimizing the length of a tuning fork
  • Five natural modes of a cantilevered wire
• Neutron diffusion
  • IAEA 2D PWR Benchmark
  • IAEA 3D PWR Benchmark
  • Cube-spherical bare reactor
  • Illustration of the XS dilution & smearing effect
• Neutron transport using $S_N$
  • Reed’s problem
  • Azmy’s problem
    • Second-order complete structured rectangular grid
    • Fist-order locally-refined unstructured triangular grid
    • Flux profiles with ray effect