https://github.com/nschloe/maelstrom

Numerical simulation of magnetohydrodynamics.
https://github.com/nschloe/maelstrom

fenics mathematics navier-stokes physics python

Last synced: about 1 month ago
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Numerical simulation of magnetohydrodynamics.

• Host: GitHub
• URL: https://github.com/nschloe/maelstrom
• Owner: nschloe
• License: mit
• Created: 2014-05-13T20:46:36.000Z (over 10 years ago)
• Default Branch: main
• Last Pushed: 2021-03-19T09:46:06.000Z (almost 4 years ago)
• Last Synced: 2024-12-26T12:11:13.670Z (about 1 month ago)
• Topics: fenics, mathematics, navier-stokes, physics, python
• Language: Python
• Homepage:
• Size: 7.43 MB
• Stars: 31
• Watchers: 6
• Forks: 6
• Open Issues: 3
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# maelstrom

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maelstrom is a numerical software tool for the solution of magnetohydrodynamics

problems in cylindrical coordinates.

As such, maelstrom includes time integrators for the heat equation, for the

Navier--Stokes equations, and a stationary solver for the Maxwell equations,

each in cylindrial coordinates.

### Some details on the problem

The goal is to compute the flux of a liquid metal under the influence of a

magnetic field, modeled by

  * the heat equation,

  * Maxwell's equations, and

  * the Navier-Stokes equations.

Heat and Navier-Stokes are coupled by buoyancy, heat and Maxwell by the Joule

effect, and Maxwell and Navier-Stokes by current induction and the Lorentz

force.

To simplify matters, it is assumed that the effect of the material flux does

not influence the electric and magnetic fields, i.e., the current induction

from moving molten metal in a magnetic field is neglected. This decouples

Maxwell's equations from the other two. Essentially, the task breaks down to

 * computing Joule heating and Lorentz force, given a voltage distribution in

   coils, and given those two quantities

 * computing the the resulting material flux inside a container.

### Solving Maxwell's equations

Derivation of the involved formulas is best taken from [the

documentation](https://maelstrom.readthedocs.io/en/master/maelstrom.maxwell.html).

##### Some visualizations

![](https://nschloe.github.io/maelstrom/magnetic-field.gif)

A typical cylindrical problem: A crucible with a liquid on the left, surrounded

by a number of electric coils (the squares). The arrows indicate the magnetic

field produced by current in those coils. Note that the actual domain where

Maxwell's equations are solved is much larger.

![](https://nschloe.github.io/maelstrom/lorentz-joule.png)

The Joule heat source (blue/red) and the Lorentz force (arrows) generated from

the above magnetic field.

![](https://nschloe.github.io/maelstrom/full.gif)

The temperature in the first 60 seconds of the full simulation. The Maxwell

equations are solved first, from this one gets the above Joule heat source and

the Lorentz force. These are added as external fources to the Boussinesq

simulation that we see here.

### Testing

To run the voropy unit tests, check out this repository and type

```

pytest

```

### License

maelstrom is published under the MIT license. See the file LICENSE for detailed

information.