Dune Ash

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Dune Ash
On display at MiMa
Type Digital
Topics Modelisation, fluid dynamics,
dynamical systems, planet Earth

Dune Ash is an exhibit from IMAGINARY, on display at MiMa and other museums.


This virtual exhibit is an interactive simulation of a volcano eruption in Europe. You can place a volcano, add a wind field and explore the ash cloud dispersing in time. The program simulates how an ash cloud emitted by a volcano moves in a certain wind field which the user can draw on a map of Europe. The wind, that is, the velocity, does not change in time, as it would happen in reality. Like that it is clear and easy to see what happens when the volcano erupts and the ash cloud is moving over Europe. The ash transport is simulated by solving a partial differential equation (PDE). The exhibit is installed on a big size touchscreen.

Activities and user interaction

The screen is divided in a left pane with the map, and a right pane with the instructions and controls. There is a restart button, or otherwise the restart is triggered after a period of inactivity.

The right panel has always the whole user instructions as an enumerated list.

  1. Choose a volcano position.
  2. Sketch a wind field.
  3. Choose a diffusion coefficient ε.
  4. Explore the simulation results.

The active step is highlighted, and the others are grey. On each step, a few controls appear or disappear from the right panel. We can move from one step to another with “back” and “next” buttons.

In Step 1, we can drag an icon on the map to choose the position. In Step 2, we can move our finger over the map to draw some lines representing the wind, the faster we move, the stronger is the wind. After this step, a computation triggers to have a wind field, that is, a vector field on each point that approximately resembles the lines introduced by hand. On Step 3 we can choose the diffusion coefficient ε, which accounts for micro-turbulences. On-screen appears the partial differential equation with the parameter ε and a brief explanation of the significance of each term. After this step, the main computation triggers, computing a source of ash particles at the volcano and integrating their trajectories across the wind field according to the diffusion equation. The computation yields a collection of frames or snapshots, that we can play as a movie, or move back and forward in time with a slider. The exhibit is self-explanatory and does not require a mediator, although if present, he/she can help stressing the applications of mathematics to understanding the Earth phenomena. This exhibit includes some research-level mathematics on the backstage, and it is not the intention to explain the equation or the numerical methods used to solve it to the public, but to show current, useful uses of mathematics and to display some of what mathematicians do today.

Mathematical background

More detailed documentation is provided by the authors, see the Resources section.

History and museology

The exhibit was developed for a “Science market” by the research team of Prof. Dietmar Kröner at Alber-Ludwigs-Universität Freiburg. The background is the eruptions of the Icelandic volcanoes Eyjafjallajökull (2010) and Grímsvötn (2011), which blocked the aerial traffic for days or weeks across Europe.

The program was presented to the math exhibits competition Mathematics of Planet Earth 2013, called by IMU and UNESCO, and organized by IMAGINARY. It was awarded the second prize. Since 2013 it is part of many regular exhibitions of IMAGINARY, and there are some permanent installations in museums, like MiMa, Deutsches Museum, Experiminta, and others.


The exhibit is released under free/open source licenses (GPL 3.0 and CC BY-NC-SA 3.0).

All the content (program and documentation) is available on its page at the IMAGINARY platform.