Project description
Efficient approaches to simulating 3D rarefied flows
The Boltzmann equation is vital for mathematical modelling of small and large physical systems, from electron transport to galactic dynamics. It can also predict rarefied gas phenomena, which are relevant to many current high-tech applications, such as microelectronics and high-altitude flight. Funded by the Marie Skłodowska-Curie Actions programme, the HYPERBOLE project will address the need for more efficient numerical methods to solve the Boltzmann equation. To enhance the simulation efficiency of 3D rarefied flows, researchers will leverage the Kronecker structure and the structural properties of the equation. The newly developed techniques will be integrated for the first time into a high-performance computing framework and applied to an industrial photolithography application.
Objective
The Boltzmann equation is highly important in mathematical modeling of physical systems large and small, from galactic dynamics to electron transport. Its range of applicability exceeds that of well-known continuum models, such as the Navier-Stokes-Fourier equations. In particular, the Boltzmann equation can accurately predict rarefied gas phenomena, which occur in a wide variety of high-tech 21st century applications, such as microelectronics, plasma physics, and high altitude flight. While numerical methods for continuum models are well established, numerical methods that accurately and efficiently solve the Boltzmann equation are undeveloped. The main objective of this research proposal is to enable three-dimensional numerical simulation of rarefied flows by developing accurate and efficient numerical solution procedures for ``the method of moments'' to numerically solve the Boltzmann equation. The approach described herein is innovative and original as it is the first to exploit Kronecker structure and structural properties of the Boltzmann equation to improve efficiency. The developed techniques will be consolidated into a high performance computing framework and applied, for the first time, to an industrial photolithography application. The proposed research involves a private-public partnership between domain experts in ``the method of moments'' at the Technical University of Eindhoven (TU/e) and experts in ``photolithography'' at ASML. If awarded, this proposal will allow me to lay the groundwork necessary to achieve a paradigm-shift in numerical simulation of rarefied gas flows. It could emanate into a successful line of research for the coming decade, with academic as well as commercial interests aligned with my career goals. I am highly motivated and uniquely positioned to carry out this research due to my specialistic expertise in efficient solution methodologies and my interdisciplinary training in mathematics, computational science and engineering.
Fields of science (EuroSciVoc)
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Keywords
Programme(s)
- HORIZON.1.2 - Marie Skłodowska-Curie Actions (MSCA) Main Programme
Funding Scheme
HORIZON-TMA-MSCA-PF-EF - HORIZON TMA MSCA Postdoctoral Fellowships - European FellowshipsCoordinator
5612 AE Eindhoven
Netherlands