Development of a polyatomic particle Fokker-Planck method for modeling of rarefied gas flows based on direct modeling

Kurzfassung

To provide a significant speedup in modeling rarefied gas flows, the collision operator in the Boltzmann equation is approximated by a Fokker-Planck operator in velocity space. A polyatomic extension of the diatomic direct modeling approach in the Fokker-Planck framework is carried out in this thesis. The model extension is verified by a code to code comparison, using DSMC data of the SPARTA code and PICLas code. Diatomic tests are performed using N2 and polyatomic tests using CO2. Temperature relaxation tests also include CH4 tests to show the capability of predicting the correct temperatures for degenerate energy modes, such as they occur in vibrtional modes in CH4. The model is verified by heat bath tests to show correct temporal relaxation into equilibrium temperatures for diatomic and polyatomic species. Two dimensional hypersonic flow tests around a cylinder investigate the particle number density as well as thermal and internal temperatures of the flow field. The relaxation of the energy for different timestep sizes and runtime efficiency for small Knudsen numbers are investigated. The diatomar relaxation process of translational and internal temperatures using N2 show very good agreement with the reference data and theoretical prediction. The polyatomic relaxation processes of the temperatures are investigated using CO2 and CH4. All relaxation tests predict the equilibrium temperature and temporal relaxations accurately. Further tests investigate the flow fields of a hypersonic flow around a cylinder by 2D simulations. The direct Fokker-Planck modeling is compared with DSMC and a FP master equation approach. The particle number density field and the temperature field is analyzed with investigations on translational, rotational and vibrational energies. The diatomic flow fields show only small deviations. The polyatomic extension approximates the shock and the overall flow field well, but shows deviations in the wake region, where the flow is rarefied. The FP direct model may be improved for rarefied regions in future works but in the context of a hybrid coupling, these regions may not use the FP direct model anyway. Finally, investigations of runtime improvements of the new modeling are made by showing a computationally more efficient model for smaller Knudsen numbers and the ability to resolve the temporal relaxation with larger timestep sizes very accurately.