Periodic Reporting for period 3 - MEDUSA (Multiscale Fluid and Plasma Dynamics using Particles)
Período documentado: 2024-01-01 hasta 2025-06-30
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.
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.
Our project has achieved significant milestones, showcasing remarkable progress in the field:
The most noteworthy accomplishment is the development of exponential integration, enabling the construction of an asymptotically preserving particle-based method on a global scale. This groundbreaking achievement allows for substantially coarser computational resolutions with maintained accuracy. As a result, we can now apply these stochastic methods in previously computationally infeasible applications due to time constraints.
The second achievement closely ties to exponential integration, as we have successfully applied this method to deterministic discrete velocity methods (DVM). This adaptability extends the second-order asymptotic preserving discretization method to both deterministic lattice-based and stochastic particle-based methods. This opens up exciting possibilities for coupling these methods, potentially harnessing the advantages of both to enhance non-equilibrium kinetic simulations of gases and plasmas.
Another significant milestone is the development of the BGK model for non-equilibrium states of internal degrees of freedom. This novel model demonstrates various advantages over existing ones and provides accurate descriptions of volume viscosity in gases. Importantly, its applicability goes beyond the particle-based models used in MEDUSA.
The entire PICLas code is, of course, open-source and fully accessible. Since the beginning of the project, new parallelization concepts have been developed and implemented, allowing the code to be efficiently utilized on modern high-performance clusters.
The most noteworthy accomplishment is the development of exponential integration, enabling the construction of an asymptotically preserving particle-based method on a global scale. This groundbreaking achievement allows for substantially coarser computational resolutions with maintained accuracy. As a result, we can now apply these stochastic methods in previously computationally infeasible applications due to time constraints.
The second achievement closely ties to exponential integration, as we have successfully applied this method to deterministic discrete velocity methods (DVM). This adaptability extends the second-order asymptotic preserving discretization method to both deterministic lattice-based and stochastic particle-based methods. This opens up exciting possibilities for coupling these methods, potentially harnessing the advantages of both to enhance non-equilibrium kinetic simulations of gases and plasmas.
Another significant milestone is the development of the BGK model for non-equilibrium states of internal degrees of freedom. This novel model demonstrates various advantages over existing ones and provides accurate descriptions of volume viscosity in gases. Importantly, its applicability goes beyond the particle-based models used in MEDUSA.
The entire PICLas code is, of course, open-source and fully accessible. Since the beginning of the project, new parallelization concepts have been developed and implemented, allowing the code to be efficiently utilized on modern high-performance clusters.
Progress beyond the state of the art:
The project has achieved significant advancements beyond the state of the art in several key areas:
Asymptotic Preserving Method: The development of exponential integration has enabled the construction of an asymptotically preserving particle-based method on a global scale. This breakthrough allows for coarser computational resolutions with maintained accuracy, making it possible to apply stochastic methods in previously computationally infeasible applications.
Adaptability to Deterministic Methods: The successful application of exponential integration to deterministic discrete velocity methods (DVM) is an important achievement. This adaptability extends the second-order asymptotic preserving discretization method to both deterministic lattice-based and stochastic particle-based methods, presenting new opportunities for coupling and enhancing non-equilibrium kinetic simulations.
BGK Model for Non-Equilibrium States: The development of a BGK model for non-equilibrium states of internal degrees of freedom and for gas mixtures. This novel model demonstrates advantages over existing ones and accurately describes volume viscosity in gases, extending its applicability beyond particle-based models.
Expected Results until the End of the Project:
By the end of the project, we anticipate the following results:
- Fully Functional Open-Source Code: The entire PICLas code will be accessible as open-source, allowing researchers and practitioners to benefit from its capabilities in non-equilibrium flow and plasma simulations.
- Robust Parallelization: The implementation of new parallelization concepts will ensure the efficient utilization of the code on modern high-performance clusters, enhancing its computational efficiency.
- Integration in Multiscale Simulations: The project aims to integrate the developed particle methods into multiscale simulations, providing a comprehensive approach to study non-equilibrium effects in gases and plasmas across different length and time scales.
- Enhanced Understanding of Non-Equilibrium Phenomena: The successful application of the developed methods will offer deeper insights into the physics of non-equilibrium flows, leading to improved understanding and prediction of complex processes in various applications.
Overall, the project's expected results will significantly advance the field of non-equilibrium simulations, enabling researchers to tackle complex and challenging problems in diverse industries and scientific domains.
The project has achieved significant advancements beyond the state of the art in several key areas:
Asymptotic Preserving Method: The development of exponential integration has enabled the construction of an asymptotically preserving particle-based method on a global scale. This breakthrough allows for coarser computational resolutions with maintained accuracy, making it possible to apply stochastic methods in previously computationally infeasible applications.
Adaptability to Deterministic Methods: The successful application of exponential integration to deterministic discrete velocity methods (DVM) is an important achievement. This adaptability extends the second-order asymptotic preserving discretization method to both deterministic lattice-based and stochastic particle-based methods, presenting new opportunities for coupling and enhancing non-equilibrium kinetic simulations.
BGK Model for Non-Equilibrium States: The development of a BGK model for non-equilibrium states of internal degrees of freedom and for gas mixtures. This novel model demonstrates advantages over existing ones and accurately describes volume viscosity in gases, extending its applicability beyond particle-based models.
Expected Results until the End of the Project:
By the end of the project, we anticipate the following results:
- Fully Functional Open-Source Code: The entire PICLas code will be accessible as open-source, allowing researchers and practitioners to benefit from its capabilities in non-equilibrium flow and plasma simulations.
- Robust Parallelization: The implementation of new parallelization concepts will ensure the efficient utilization of the code on modern high-performance clusters, enhancing its computational efficiency.
- Integration in Multiscale Simulations: The project aims to integrate the developed particle methods into multiscale simulations, providing a comprehensive approach to study non-equilibrium effects in gases and plasmas across different length and time scales.
- Enhanced Understanding of Non-Equilibrium Phenomena: The successful application of the developed methods will offer deeper insights into the physics of non-equilibrium flows, leading to improved understanding and prediction of complex processes in various applications.
Overall, the project's expected results will significantly advance the field of non-equilibrium simulations, enabling researchers to tackle complex and challenging problems in diverse industries and scientific domains.