Welcome to pyISFenix docs#

pyISFenix: PYthon framework for the Incompressible Schrodinger Flow using FENIcsX

Authors: Stefano Riva, Carolina Introini, Antonio Cammi

The simulation of fluid dynamics is typically carried out either under the hypothesis of continuum matter (state-of-the-art Computational Fluid Dynamics) or adopting a particle perspective in Lattice Boltzmann methods; however, back in the early 1920s, while quantum mechanics theory was being developed, Erwin Madelung published a paper [Mad26] in which an analogy between the Schrödinger equation and the Euler equations, describing the motion of inviscid flows. Thus, a transfomation exist linking wave functions and flow fields.

This approach has been recently re-discovered by Albert Chern in [Che17, CKP+16], who published a numerical implementation of the Madelung transformation, enabling the simulation of incompressible inviscid fluids using an correspondent wave function. This novel methodology is known as Incompressible Schrödinger Flow (ISF): the original implementation has been later extended by the authors to a Finite Element solution by the authots in [RIC24]; in particular, the FEniCSx library in Python is used to solve the steps of the ISF algorthm.

This documentation includes a brief introduction to the algorithm and the basis theory behind, the API documentation of the solvers and some case studies reported in the published papers.

This work has been carried out at the Nuclear Reactors Group at Politecnico di Milano, under the supervision of Prof. Antonio Cammi.

How to cite#

If you are going to use this implementation of ISF in your research work, please cite the following articles

Riva, S., Introini C., Cammi A., ‘A Finite Element Implementation of the Incompressible Schrödinger Flow Method’. Physics of Fluids, 2023.

Installation notes#

The package has been tested on MacOS and Ubuntu 18.04/20.04 machines with Python3.10.

Dependencies#

The ISF solvers requires the following dependencies:

import numpy
import h5py

import pyvista
import gmsh
import dolfinx

Be sure to install gmsh and gmsh-api before dolfinx=0.7.2 (the package has been tested with real mode of the PETSc library). The instructions to install dolfinx are available at FEniCS/dolfinx.

Set up a conda environment for ISF#

At first create a new conda environment

conda create --name <env_name>

If not already done, add conda-forge to the channels

conda config --add channels conda-forge

After having activate it, install

conda install python=3.10

This provides also pip which is necessary to install gmsh as

python -m pip install gmsh gmsh-api

Now, install dolfinx (the current version works with version 0.7.2, an update to version 0.8.0 is under development)

conda install fenics-dolfinx=0.7.2 petsc=*=complex* mpich pyvista

Add the following packages

conda install meshio tqdm

Downgrade the following

python -m pip install setuptools==62.0.0
conda install numpy=1.23.5

Once this is completed, it may be necessary to re-install gmsh

python -m pip install gmsh gmsh-api

How to use the solvers?#

Once all the dependencies have been installed, the classes in src folder can be imported and used to solve ISF.