A spectral element method based on the hierarchical Poincaré-Steklov scheme and its application to modelling non-equilibrium atmospheric-pressure plasmas

• Applicant: Dr. Igor Semenov
• Subject Area: Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas ; Mathematics
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 515939493

Non-equilibrium atmospheric-pressure plasmas are used in many plasma-assisted technologies. In particular, this kind of gas discharge plays an important role in plasma-chemical applications such as plasma-stimulated wound healing, conversion of greenhouse gases and plasma electrolysis. Some of these topics are especially relevant to the transition to sustainable energy systems. Numerical modelling helps to understand the physics and chemistry of non-equilibrium atmospheric-pressure plasmas and thereby supports the development of new plasma applications. However, simulating these discharges is very challenging, because they are intrinsically multiscale in nature. The complexity of the problem further increases when a realistic geometry of the plasma source needs to be taken into account. The goal of this project is to explore whether the use of a novel numerical technique - the hierarchical Poincarè-Steklov (HPS) scheme – can help to improve computational efficiency in modelling non-equilibrium atmospheric-pressure plasmas. The HPS scheme is a method for solving elliptic partial differential equations, which belongs to the family of spectral element methods. In comparison to the existing methods, the HPS scheme simplifies the use of adaptive mesh refinement and non-overlapping domain decomposition, especially on unstructured computational meshes. In addition, the HPS has good convergence properties and is easy to program and to parallelize. The properties of the HPS scheme are very beneficial for solving multiscale problems in complex geometries. It can be expected that the use of this method will reduce the computational cost of atmospheric-pressure plasma models and will extend the range of problems addressed in related computational studies. It has been shown recently, that the HPS scheme provides an efficient strategy for simulating streamer discharges on structured grids. In this project, the HPS scheme for solving two-dimensional elliptic problems on unstructured meshes will be developed and applied to modelling certain technologically relevant discharges. It will be also explored how the HPS scheme can be combined with the discontinuous Galerkin method to simulate the discharge evolution over time efficiently. As particular examples, streamer discharges between parabolic electrodes and plasma dynamics in a cold atmospheric-pressure plasma jet will be simulated. The advantages of using the HPS scheme for the development of one-dimensional plasma models will be explored as well on the example of a dielectric-barrier discharge.

• DFG Programme: Research Grants