MattFlow

<br />

A CFD python package for the Shallow Water Equations

MattFlow simulates the surface of the water after any initial conditions, such as drops or stones falling on.

<img src="https://media.giphy.com/media/jpVKPxzBiGoSvNYUrY/giphy.gif" width="265" height="150" /> <img src="https://media.giphy.com/media/VJNqBY7uKP3r0AvCcp/giphy.gif" width="265" height="150" /> <img src="https://media.giphy.com/media/QxYpANpE5snKSrdLJ5/giphy.gif" width="265" height="150" />

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| requirements | os | | -------------------- | --------- | | python3 | GNU/Linux | | click >= 7.0 | Windows | | joblib >= 0.13.2 | OSX | | matplotlib >= 3.3.1 | | | numba >= 0.51.2 | | | numpy >= 1.18.5 | | | ffmpeg (optional) | |

Install

$ conda create --name mattflow -y
$ conda activate mattflow
$ conda install -c mattasa mattflow

$ pip install mattflow

Usage

$ mattflow [OPTIONS]

Options:
  -m, --mode [drop|drops|rain]    [default: drops]
  -d, --drops INTEGER             number of drops to generate  [default: 5]
  -s, --style [water|contour|wireframe]
                                  [default: wireframe]
  --rotation / --no-rotation      rotate the domain  [default: True]
  -b, --basin                     render the fluid basin
  --show / --no-show              [default: True]
  --save
  --format [mp4|gif]              [default: mp4]
  --fps INTEGER                   [default: 18]
  --dpi INTEGER                   [default: 75]
  --fig-height INTEGER            figure height (width is 1.618 * height)
                                  [default: 18]
  --help                          Show this message and exit.

Shallow Water Equations

SWE is a simplified CFD problem which models the surface of the water, with the assumption<br /> that the horizontal length scale is much greater than the vertical length scale.

SWE is a coupled system of 3 hyperbolic partial differential equations, that derive from the<br /> conservation of mass and the conservation of linear momentum (Navier-Stokes) equations, in<br /> case of a horizontal stream bed, with no Coriolis, frictional or viscous forces (wiki).

<img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b9d481407c0c835525291740de8d1c446265ce2" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -18ex; width:46ex; height:19ex;" alt="{\displaystyle {\begin{aligned}{\frac {\partial (\rho \eta )}{\partial t}}&amp;+{\frac {\partial (\rho \eta u)}{\partial x}}+{\frac {\partial (\rho \eta v)}{\partial y}}=0,\\[3pt]{\frac {\partial (\rho \eta u)}{\partial t}}&amp;+{\frac {\partial }{\partial x}}\left(\rho \eta u^{2}+{\frac {1}{2}}\rho g\eta ^{2}\right)+{\frac {\partial (\rho \eta uv)}{\partial y}}=0,\\[3pt]{\frac {\partial (\rho \eta v)}{\partial t}}&amp;+{\frac {\partial (\rho \eta uv)}{\partial x}}+{\frac {\partial }{\partial y}}\left(\rho \eta v^{2}+{\frac {1}{2}}\rho g\eta ^{2}\right)=0.\end{aligned}}}">

where:<br /> η : height<br /> u : velocity along the x axis<br /> υ : velocity along the y axis<br /> ρ : density<br /> g : gravity acceleration

Structure

1. pre-process<br /> structured/cartesian mesh
2. solution<br /> supported solvers:
   • Lax-Friedrichs Riemann    | O(Δt, Δx², Δy²)
   • 2-stage Runge-Kutta         | O(Δt², Δx², Δy²)  | default
   • MacCormack           | O(Δt², Δx², Δy²)  | experimental
3. post-processing<br /> matplotlib animation

Configuration options

• mesh sizing
• domain sizing
• initial conditions (single drop, multiple drops, rain)
• boundary conditions (currently: reflective)
• solver
• multiprocessing
• plotting style
• animation options

TODO

1. GUI
2. Cython/C++
3. Higher order schemes
4. Source terms
5. Viscous models
6. Algorithm that converts every computational second to a real-time second, modifying the fps at<br />the post-processing animation, because each iteration uses a different time-step (CFL condition).
7. Moving objects inside the domain
8. 3D

License

GNU General Public License v3.0 <br /> <br />

Special thanks to Marios Mitalidis for the valuable feedback.

<br />

Start the flow!

(C) 2019, Athanasios Mattas<br /> thanasismatt@gmail.com