Development and application of particle methods at DLR Spacecraft department
GM. Grabe, L. Basov, M. Ertl, Spacecraft Department German Aerospace Center (DLR) 37073 Göttingen, Germany martin.grabe@dlr.de
The Spacecraft department in the DLR Institute for Aerodynamics and Flow Technology conducts research and development on a wide array of spacecraft aerothermodynamic problems. It operates large-scale test facilities for high-enthalpy hypersonic flows and high-vacuum plume test facilities for chemical and electric orbital propulsion. The experimental capabilities are complemented by high-fidelity in-house Navier-Stokes solvers “TAU” and “CODA”, as long as the associated flow problems are characterized by sufficiently low Knudsen number. Driven by the need to study more rarefied flows with high computational efficiency on an engineering-scale, we rely on the Direct Simulation Monte Carlo (DSMC) code SPARTA, developed at Sandia National Laboratories. A number of technically relevant flow scenarios involve domains of both high and low Knudsen number. While the DSMC method correctly models gas flows with low Knudsen number, it is attractive to hybridize it with a numerical scheme that computes these flows more efficiently. The particle-based Fokker-Planck method appears to be a natural choice, as it essentially only replaces the collision step in DSMC with an alternate scheme of momentum and energy redistribution that does not rely on evaluating binary collisions. In this talk, we present an overview of recent developments, extensions, and applications of the particle-based Fokker-Planck method carried out at DLR Göttingen. The original method [1, 2] has been extended to model gas mixtures [3], internal energy redistribution in diatomic [4] and polyatomic [5] species, and recently also gas-phase chemical reactions [6], while maintaining compatibility with models customarily used in DSMC. We show application examples in which the Fokker-Planck solutions are compared with those of DSMC and Navier-Stokes, and discuss the need for further development.
[1] Jenny, Torrilhon, and Heinz. “A Solution Algorithm for the Fluid Dynamic Equations Based on a Stochastic Model for Molecular Motion.” Journal of Computational Physics 229, no. 4 (February 2010): 1077–98. https://doi.org/10/bt65m7.
[2] Gorji, Torrilhon, and Jenny. “Fokker–Planck Model for Computational Studies of Monatomic Rarefied Gas Flows.” Journal of Fluid Mechanics 680 (August 10, 2011): 574–601. https://doi.org/10.1017/jfm.2011.188.
[3] Hepp, Grabe, and Hannemann. “A Kinetic Fokker–Planck Approach to Model Hard-Sphere Gas Mixtures.” Physics of Fluids 32, no. 2 (February 1, 2020): 027103. https://doi.org/10.1063/1.5141909
[4] Hepp, Grabe, and Hannemann. “Master Equation Approach for Modeling Diatomic Gas Flows with a Kinetic Fokker-Planck Algorithm.” Journal of Computational Physics 418 (October 2020): 109638. https://doi.org/10.1016/j.jcp.2020.10963
[5] Basov and Grabe. “Modeling of Polyatomic Gases in the Kinetic Fokker-Planck Method by Extension of the Master Equation Approach.” In AIP Conf. Proc., 2996:060004. Seoul, Republic of Korea: AIP, 2024. https://doi.org/10.1063/5.0187658.
[6] Basov, Oblapenko and Grabe. “Modeling of Chemical Reactions in Rarefied Gas Flows by the Kinetic Fokker-Planck Method.” Physics of Fluids (in press).