StokesMFS is three-dimensional Stokes-flow solver that uses the Method of Fundamental Solutions (MFS). It can simulate almost any arbitrary particle with vanishing Reynolds number. This work is a Python implementation of some of the methodology published in [1], which is a continuation of the work in [2]. The main focus of this repository is flow visualisation.
This code requires numpy and matplotlib, to install these with Linux:
sudo pip install numpy
sudo pip install matplotlib
The guide document 'pythonMFS Guide.pdf' contains all the background and explanation of how to run the code. All you need for a MFS simulation is contained within the file pythonMFS.py. The file examples.py contains 5 examples which cover: calculation of force and torque, two flow visualisation methods, and an investigation into numerics. The examples are written to be readable and editable as much as possible, it is quite a sandbox.
The main functions in pythonMFS.py of note are:
constructMatrix(rb,rs)constructs the matrix of linear equations to be solved.constructRHS(rb,v,om)constructs the super-vector of boundary conditions.
These are the only functions required to simulate a particle, whose boundary is discretised into a number of nodes given by rb, with internal sites given by rs, which has translational velocity v and angular velocity om. You can easily simulate any particle if you can create rb and rs, by using import pythonMFS as mfs and using these two functions.
- Dynamic simulation of particles. For example, animation of a sphere settling under gravity.
- Improved speed for multi-particle simulations. This has been implemented in MATLAB for [1], and the methodology can be seen in that paper.
- Inclusion of rarefaction effects, starting with the G13 equations, possibly moving on to the R13 equations, or even the R26.
This work is based on work supported by the Engineering and Physical Sciences Research Council: [EP/N016602/1] and [EP/V01207X/1].
[1]. Josiah J.P. Jordan and Duncan A. Lockerby. “The method of fundamental solutions for multi-particle Stokes flows: Application to a ring-like array of spheres”. In: Journal of Computational Physics 520 (2025), p. 113487. doi.org/10.1016/j.jcp.2024.113487
[2]. Duncan A. Lockerby and Benjamin Collyer. “Fundamental solutions to moment equations for the simulation of microscale gas flows”. In: Journal of Fluid Mechanics 806 (2016), p. 413-436. doi.org/10.1017/jfm.2016.606