Non-equilibrium effects in fluid and plasma dynamics are crucial for understanding the physics and optimising industrial applications, as future industrial processes and applications will generally be further miniaturised (semiconductor industry) or the energy required will continue to increase (e.g. extreme ultraviolet lithography (EUV)), leading to shorter timescales. 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 with the computational simulation of these applications is that a non-equilibrium state of gases or plasmas cannot be clearly defined because it is used and measured differently by different communities and applications. 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 or translational DOFs, rotational or translational DOFs for molecules. Non-equilibrium can be the result of chemical reactions occurring in the flow field and changing the chemical composition (chemical non-equilibrium) with the ionisation process as a special type of reaction where the neutral gas flow is additionally transformed into an even more complex plasma flow. 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 equilibrium breaks down. In addition to non-equilibrium as a result of high process energies and rarefied gases, it can also occur when the spatial dimensions become very small, as is the case in and nanosystems, which are already playing an important role in the semiconductor industry.
It also has implications for biotechnology and laser-based materials processing. In addition, in the aerospace industry, non-equilibrium simulations are important for applications such as hypersonic atmospheric entry, vacuum expansion and electric space propulsion systems. Furthermore, non-equilibrium effects play a crucial role in vacuum technology, which includes applications such as vacuum chambers and pumps.
At present, simulation tools for non-equilibrium effects are only available for very specific types of applications, depending on the prevailing definition of non-equilibrium.
However, this lack makes the research and development of new technologies very cumbersome, since the available numerical methods cannot be used in a predictive way if the type of non-equilibrium is not known a priori. The aim of the MEDUSA (MultiscalE Fluid and plasma Dynamics USing pArticles) project is to develop and extend the open-source, multi-scale particle code PICLas, available for use in a variety of fields, which will consolidate the broad 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 domain. 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 flux and pressure tensor. The most general solution, however, is to describe the particle distribution in the gas itself, instead of the average values of this distribution, which just 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 even more dimensions that must be considered, and this should also be done for the different species if possible. As a consequence, one has a very highly dimensional problem with many degrees of freedom, which can be solved particularly efficiently with stochastic particle methods.
The main objectives to be worked on and achieved within MEDUSA are as follows:
1. Asymptotic preserving (AP) particle methods: Developing efficient particle methods that can handle rarefied and continuum regions with the same time step size is a key ch allenge. An AP method would enable more efficient non-equilibrium flow and plasma simulations, allowing simulations of much more complex applications.
2. Multi-species models. Especially in the asymptotic preserving method to be developed, the handling of multispecies mixtures and chemical reactions is relatively unclear, but essential for a variety of industrial and space applications. Therefore, such models are to be developed on the basis of different modelling approaches.
3. Statistical noise reduction: A major disadvantage of stochastic particle methods is the inherent stochastic noise of the methods themselves. This leads to very poor noise-signal ratios, especially in simulations with small Mach numbers or velocities, and thus to greatly extended simulation times. Therefore, alternative methods for noise reduction are to be developed here.
4. Multiscale simulation of plasma flows: Plasma conditions involve complex interactions between charged particles, requiring computationally expensive evaluations. Handling the large difference in masses between electrons and heavy particles remains a challenge. Developing a satisfactory solution would be crucial for understanding non-equilibrium plasmas, which will shape the future application landscape.
