A finite-element solution of the Reynolds equation with a cavitation model.
This module implements the stabilized finite-element approach published in [1] in the finite-element framework Gridap [2] written in Julia. The code complements the paper and can be used to reproduce the results presented there. Whenever possible, it uses the same notation and refers to the equation numbers so that the code and paper can be easily followed.
Note: The results published in the paper were not created by this code but by a prototype in Matlab. Hence, small differences in the computed errors and residuals can occur when compared with the figures in the paper. Also, the shock-capturing approach described in the paper has not yet been included in the Gridap implementation.
I closely followed the Gridap tutorials at github.com/gridap/Tutorials to implement this application. They are great if you want to get started using Gridap.
- 'GridapReynoldsEquation.jl': main file of the module
- 'Reynolds_functions.jl': contains basically all functions defining the problem, the definition of the partial differential equation, domain, finite-element spaces, as well as functions for plotting and performing a convergence test.
- 'testRuns*.jl': needed for precompilation using PrecompileTools.
- 'ReynoldsExampleLoads.jl': defines loads, analytical solutions, boundary conditions, initial conditions for the three examples as in the paper. The loads have been computed using the Matlab program Manufactured solutions [3].
- 'example*.jl' are the input files and main scripts to run in order to reproduce the examples
- 'results' contains the 'state' files for plotting the results in Paraview (optional).
- Julia
- Paraview (recommended) for plotting the results
running the examples:
Provided you have Julia installed, you should be able to simply download this repository and run the example files.
Details for those new to Julia:
- download or clone this repository
- open a terminal in the main folder GridapReynoldsEquation and start Julia
- start the package manager by typing:
] - activate the project by typing:
activate . - install/update dependencies by typing:
instantiate - wait while Julia installs all missing packages (may take a while)
- run one of the example* files (in Terminal e.g.
include("example81_82.jl"))
Instead of using the terminal for everything, you may want to use an environment such as VScode with the Julia extension, allowing you to run the example with a click.
Running the code for the first time takes significantly longer due to compilation, which is normal behavior in Julia. The second time takes a few seconds on my desktop computer to run the complete convergence test for examples 1 or 2.
note: With the update on 2023/10/10, PrecompileTools are used for efficiency. This results in rather long compilation times when running the code for the very first time. A compiled version of the module's functions is stored during this process so that the startup and compilation times are drastically reduced for any future uses. Should you encounter any problems with this procedure, you may use a previous commit (e.g. f4809aa16afc626c6ebe800161b9740a4b4ef334), which is fully functional but requires some extra compilation time after every restart or even change in the input file.
plotting results The meshes and results are written in .vtu format in the subfolders of the 'results' folder. They can easily be plotted using Paraview. If you like, you can use the "state" files (.pvsm) provided in the results folder. Load them using File->load state, choose 'Search files under specified directory', and make sure to select the directory containing the corresponding .vtu files.
note: The folders for writing the results are not created automatically; they must already exist.
[1] Gravenkamp, H., Pfeil, S., Codina, R., Stabilized finite elements for the solution of the Reynolds equation considering cavitation, Computer Methods in Applied Mechanics and Engineering (2023)
[2] Gridap, https://gridap.github.io/Gridap.jl/stable/
[3] Gravenkamp, H., Manufactured solutions (2023). doi:10.5281/zenodo.8315789. 20
Gravenkamp, H., Gridap Reynolds Equation, 2023, doi:10.5281/zenodo.8407785
