# Multiscale models help solve huge problems

2021-06-08Knowing how long stored carbon dioxide stays in the ground or how the groundwater flows below the ground surface are difficult questions to answer. Mathematical calculations often become so complicated that computers cannot handle them.

This kind of research began in the 1970s when oil and gas were to be extracted in the North Atlantic. Omar Richardson, a new doctor of mathematics at Karlstad University, has in his dissertation "Multiscale models and simulations for diffusion and interaction in heterogeneous domains" researched how mathematical models can provide answers to complicated questions.

- My research can, for example, add knowledge to those who try to store carbon dioxide from the atmosphere in the soil reducing the effects of climate change. Placing it there is one thing, but knowing how long it will stay in storage is another. Predicting it is very complicated. The gas will hide in the pores of the stones but over time it will move. It can take different lengths of time - decades or centuries.

Omar Richardson's research is based on making multi-scale mathematical models in order to be able to deal with these complicated calculations.

- I try to show real structures and phenomena with my research, says Omar Richardson. How many buses do you need in a medium-sized city? How does a waterfall impact a river bed? There are various examples around which you can build mathematical models.

The predict is to look at a real process, in this case the flow of groundwater. Doing underground measurements is a lot of work, but gaining insight in groundwater flows is vital from a natural and a societal aspect. This is where mathematical models can help.

However, if you look at what is happening below the earth's surface, there are enormous areas to deal with. Water, gas and oil are mixed with rock and sand with different surface structures. Making a mathematical model to investigate how, for example, groundwater is transported under the ground in Värmland would be so enormous that it would be impossible to run it in a computer simulation. That's a problem.

- So, this is where my research on multi-scale models comes in, Omar explains. Microscopic differences in the rock surface layer have a large effect on the water that flows past it - some absorb water, some repel water - a model is needed that can work based on these differences.

A multiscale model is built up from layers of different sizes, combining for instance a layer of molecules with a layer of cells. One of the challenges is how to translate information from small-scale layers to large-scale layers and back.

- My focus was to make multiscale technology available to different applications and fields. While the models are still in development, we have seen big improvements in efficacy compared to conventional models.

## Is there anything in your research you want to continue with?

- A fun part of my research was to apply these techniques to models of moving crowds. I constructed a simulation where a building was full of people. Only part of these people knew what the building looked like, and the others had to guess, or follow their neighbors. It was interesting to see how the building was evacuated in different situations. It becomes practical and you see what it is you have worked with. It would be fascinating to explore the multiscale aspects of crowd dynamics further.