The RWTH Aachen has a B.Sc. and M.Sc. program called Computational Engineering Science (CES). It combines math, physics, computer science and engineering. The overall idea is that by the end of your studies, you can *do something with simulations* (at least that is my opinion). And *something *includes a lot. People end up in aerospace engineering, computer vision, finance, the automotive industry, logistics or medical engineering to name just some examples.

I started to study CES, because I didn’t know what to do with a mathematics degree. At least I didn’t know it back then. Mechanical engineering was *too practical *and for computer science I lacked the coding experience (also not necessary but I thought it was). Physics seemed equally interesting but CES caught me with their fancy pictures and videos of simulations.

Below are two examples of stuff I did during my studies. Once an attempt to implement the Lattice-Boltzmann method and secondly a Monte-Carlo simulation for radiation therapy. Obviously, both of these implementations are very basic and only serve the purpose to demonstrate what can possibly be done. I wouldn’t trust my student skills (or even my skills nowadays) and rely on these flow computations or dose calculations.

### Example 1: CFD with Lattice-Boltzmann

This method is one way to compute the airflow around objects, for example cars or wings. The basic idea is to discretize the domain and let air flow along certain directions. If the air hits a wall it gets reflected, if the pressure is high, air flows different from flow within a vacuum. After computing the flow field, we can trace the trajectories of air particles that enter the domain (in the pictures below from the left). We see how they move around the objects and get compressed (which is due to falsely putting a wall on top of the domain too). From these computations, drag coefficients can be computed. Here we see the flow simulation for a VW Beetle and a Lamborghini, shown at the top of the page and below, respectively.

Maybe a more reasonable computation is shown below. Air flows around an airfoil from the lower left to the upper right region. An important coefficient that can be computed here is the lift.

All the implementations where done for a lecture “Lattice-Boltzmann methods” within the CES program as exercises. Where we learned about the mathematical theory, as well as how to implement these procedures within a numerical tool.

### Example 2: Radiation therapy with Monte-Carlo

A second possible application arises in the medical sector. Let’s say someone has a tumor and we want to do radiation therapy. The idea is to shoot high energetic particles at the tumor and destroy it that way. Therefore, we want to know how the radiation distributes in the body. Let’s say we have a scan of the region of interest, shown on the right. Now we shoot particles in the direction of the tumor and trace their trajectories. These particles scatter in the body (i.e. they interact with the tissue or the bones), while they might stream freely in the lungs. The particles are being absorbed which is the energy transfer to the tissue that hopefully destroys the tumor.

If we now simulate several particles that move (semi-)randomly through the body, we can color the regions with many particles in yellow and regions with fewer particles in blue, shown on the right. Here, we shoot from the upper left corner and most particles are being absorbed just after the body, however there is a lot of scattering. I would again not trust these simulations because I did not bother to look up the real absorption or scattering coefficients and this is just a 2d simulation, but the general idea is the same as in more sophisticated tools that are being used in industry.