# MEDUSA - Multiscale Fluid and Plasma Dynamics using Particles

ERC Starting Grant

The objective is to develop particle-based multiscale methods for thermo-chemical non-equilibrium gas and plasma flows, which for the first time enable the simulation of a large number of high-tech applications.

Non-equilibrium effects in fluid and plasma dynamics are crucial for the understanding of physics and the optimization of industrial applications, as future industrial processes and applications will usually be further miniaturized (semiconductor industry) or the energy demand will continue to increase (e.g. extreme ultraviolet lithography (EUV)), leading to shorter time scales. This makes experimental measurements difficult, impossible or very expensive. To overcome these problems and reduce costs, the ability to simulate non-equilibrium effects in gases and plasmas is essential. The main problem in simulating these applications is that a non-equilibrium state of gases or plasmas cannot be clearly defined, as the term is used and measured differently in different applications and the corresponding communities. A system can be in a non-equilibrium state if the boundaries interacting with the gas or plasma are not in (chemical) equilibrium with the gas/plasma. A non-equilibrium state can also be described by different degrees of freedom (DOFs) within the gas or plasma, e.g. vibrational, rotational or translational DOFs for molecules.

The non-equilibrium can be the result of chemical reactions that take place in the flow field and change the chemical composition (chemical non-equilibrium), with the ionization process being a special type of reaction in which the neutral gas is additionally transformed into an even more complex plasma. Finally, even the concept of temperature can become problematic in highly rarefied flows, such as those found at high altitudes and in industrial vacuum chambers, where the equilibrium assumptions are no longer valid. In addition to non-equilibrium due to high process energies and dilute gases, it can also occur when the spatial dimensions become very small, as is the case with nanosystems, which already play an important role in the semiconductor industry.

This also has implications for biotechnology and laser-based material processing. In the aerospace industry, non-equilibrium simulations are important for applications such as atmospheric entry, vacuum expansions and electric space propulsion. Furthermore, non-equilibrium effects play a crucial role in vacuum technology, which includes applications such as vacuum chambers and pumps.

Currently, simulation tools for non-equilibrium effects are only available for very specific types of applications, depending on the prevailing definition of non-equilibrium.

This lack, however, complicates the research and development of new technologies, since the available numerical methods cannot be used predictively if the type of non-equilibrium is not known a priori. The aim of the MEDUSA project (MultiscalE Fluid and plasma Dynamics USing pArticles) is to develop and extend the open-source multiscale particle code PICLas, which can be used in a variety of fields and summarizes the wide range of non-equilibrium effects for the predictive simulation of future high-tech applications.

Stochastic particle methods were chosen for the project mainly because they offer some advantages in the non-equilibrium range. Gases in strong non-equilibrium are no longer correctly described by a few macroscopic values such as density, velocity and temperature, but must be described by additional quantities such as heat flow and pressure tensor. However, the most general solution is to describe the particle distribution in the gas itself and not the average values of this distribution, which only correspond to the macroscopic values mentioned. This means that in the case of the particle distribution, at least three velocity dimensions must be added to the three spatial dimensions. In addition, the internal energies of the particles form further dimensions that must be taken into account, and this should also be done for the various species present in gases if possible. We therefore have a very high-dimensional problem with many degrees of freedom, which can be solved particularly efficiently using stochastic particle methods.

## Various applications simulated with PICLas

## The main objectives of MEDUSA

The development of efficient particle methods that can treat both rarefied and continuum regions with the same time step size is a key challenge. An AP method would enable more efficient non-equilibrium flow and plasma simulations, allowing simulations of much more complex applications.

Especially for the AP methods to be developed, the treatment of multispecies mixtures and chemical reactions is relatively unclear, but essential for a variety of industrial and aerospace applications. Therefore, such models will be developed based on different modeling approaches.

A major disadvantage of stochastic particle methods is the inherent stochastic noise of the methods themselves. This leads to very poor noise-to-signal ratios, particularly in simulations with small Mach numbers or velocities, and thus to greatly increased simulation times. For this reason, alternative methods for noise reduction are to be developed here, e.g. the coupling of stochastic and deterministic methods.

Plasma conditions involve complex interactions between charged particles that require computationally intensive evaluations. Dealing with the large mass difference between electrons and heavy particles remains a challenge. Developing a satisfactory solution would be crucial for understanding non-equilibrium plasmas, which are essential for the future application landscape.

## Plasma Kinetic Code PICLas

All models developed within the numerics group are available on GitHub in the open source code PICLas. In addition, detailed documentation can be found at piclas.readthedocs.io.

### Contact

### Marcel Pfeiffer

**Dr.-Ing.**