CFD Julia

A Julia adaptation of CFDPython Copyright (c) Barba group - https://github.com/barbagroup/CFDPython

cite: Barba, Lorena A., and Forsyth, Gilbert F. (2018). CFD Python: the 12 steps to Navier-Stokes equations. Journal of Open Source Education, 1(9), 21, https://doi.org/10.21105/jose.00021

CFD Julia adapts CFD Python, a.k.a. the 12 steps to Navier-Stokes to the Julia programming language. CFD Python is a practical module for learning the foundations of Computational Fluid Dynamics (CFD) by coding solutions to the basic partial differential equations that describe the physics of fluid flow. The module was part of a course taught by Prof. Lorena Barba between 2009 and 2013 in the Mechanical Engineering department at Boston University (Prof. Barba since moved to the George Washington University).

The module assumes only basic programming knowledge (in any language) and some background in partial differential equations and fluid mechanics. The "steps" were inspired by ideas of Dr. Rio Yokota, who was a post-doc in Prof. Barba's lab until 2011, and the lessons were refined by Prof. Barba and her students over several semesters teaching the CFD course.

Guiding students through these steps (without skipping any!), they learn many valuable lessons. The incremental nature of the exercises means they get a sense of achievement at the end of each assignment, and they feel they are learning with low effort. As they progress, they naturally practice code re-use and they incrementally learn programming and plotting techniques. As they analyze their results, they learn about numerical diffusion, accuracy and convergence. In about four weeks of a regularly scheduled course, they become moderately proficient programmers and are motivated to start discussing more theoretical matters.

How to use this module

In a regular-session university course, students can complete the CFD Python/CFD Julia lessons in 4 to 5 weeks. As an intensive tutorial, the module can be completed in two or three full days, depending on the learner's prior experience. The lessons can also be used for self study. In all cases, learners should follow along the worked examples in each lesson by re-typing the code in a fresh Jupyter notebook, maybe taking original notes as they try things out.

Lessons

Launch an interactive session with this module using the Binder service:

Steps 1–4 are in one spatial dimension. Steps 5–10 are in two dimensions (2D). Steps 11–12 solve the Navier-Stokes equation in 2D. Three "bonus" notebooks cover the CFL condition for numerical stability, array operations with NumPy, and defining functions in Python.

• Quick Julia Intro —For Julia novices, this lesson introduces Julia and covers the fundamentals required in this mini-course.
• Step 1 —Linear convection with a step-function initial condition (IC) and appropriate boundary conditions (BCs).
• Step 2 —With the same IC/BCs, nonlinear convection.
• CFL Condition —Exploring numerical stability and the Courant-Friedrichs-Lewy (CFL) condition.
• Step 3 —With the same IC/BCs, diffusion only.
• Step 4 —Burgers’ equation, with a saw-tooth IC and periodic BCs (with an introduction to Sympy).
• Array Operations with Julia
• Step 5 —Linear convection in 2D with a square-function IC and appropriate BCs.
• Step 6 -With the same IC/BCs, nonlinear convection in 2D.
• Step 7 -With the same IC/BCs, diffusion in 2D.
• Step 8 -Burgers’ equation in 2D
• Defining Functions in Python
• Step 9 -Laplace equation with zero IC and both Neumann and Dirichlet BCs.
• Step 10 -Poisson equation in 2D.
• Step 11 -Solves the Navier-Stokes equation for 2D cavity flow.
• Step 12 -Solves the Navier-Stokes equation for 2D channel flow.

Dependencies

To use these lessons, you need Julia, add the following dependencies: . Jupyter—an interactive computational environment that runs on a web browser, is also required.

This mini-course is built as a set of Jupyter notebooks containing the written materials and worked-out solutions in Julia code. To work with the material, we recommend that you start each lesson with a fresh new notebook, and follow along, typing each line of code (don't copy-and-paste!), and exploring by changing parameters and seeing what happens.

Installing Julia

Platform specific installation instruction for the Julia language can be found at the official Julia language website: Install Instructions.

Installing CFDJulia's dependencies

Julia provides environments to ensure dependencies are consistent for all users of a project such as CFDJulia. To use CFDJulia's environment first clone the repository:

git clone http://https://github.com/Cysor/CFDJulia.git

Then navigate to the cloned CFDJulia directory and run the following commands to install CFDJulia's dependencies.

julia

julia>
julia>]
(@v1.x) pkg>
(@v1.x) pkg> activate .
(CFDJulia) pkg> instantiate
(CFDJulia) pkg> [backspace]
julia>

Running the notebook server

Once the CFDJulia's dependencies have been installed jupyter notebook can be started using the the following commands entered into the already open julia instance as follows:

julia> using IJulia
julia> notebook()

or if you prefer to use jupyter lab:

julia> using IJulia
julia> jupyterlab()

If you do not have jupyter installed julia will prompt you to install it via miniconda as shown bellow:

julia> notebook()
install Jupyter via Conda, y/n? [y]: y

This will start up a Jupyter session in your browser!

How to contribute to CFD Julia

We accept contributions via pull request. You can also open an issue if you find a bug, or have a suggestion.

Copyright and License

(c) 2020 Cysor. All content is under Creative Commons Attribution CC-BY 4.0, and all code is under BSD-3 clause.

We are happy if you re-use the content in any way!