Modeling of internal energy modes within a kinetic Fokker-Planck algorithm

Abstract

The Direct Simulation Monte Carlo (DSMC) method is widely used to model non-equilibrium rarefied gas flows, such as shock waves or strong expansion flows. However, its application to practical problems at rather high density is costly, as the computational effort for DSMC increases strongly with decreasing Knudsen number. It is therefore common practice to couple DSMC with less accurate, but faster methods, applying those to flow domains in which the resolution and modeling depth of DSMC is not required. One recently proposed method employs a kinetic Fokker-Planck (FP) model. The FP method employs a large number of simulator particles that are moved through the computational domain, and updates particle velocities in a separate step, as is the case in the DSMC method. These algorithmic similarity fosters a simple coupling of both methods. Correct modeling of internal energy modes is relevant for simulating non-equilibrium molecular flow. While well-established models for internal energy relaxation exist for DSMC, only few approaches are documented in the open literature for the FP method. In particular, according to the authors’ knowledge, no models for describing discrete internal energy levels within FP have yet been developed. In this talk, a scheme is presented to extend arbitrary monatomic Fokker-Planck models to describe polyatomic species. A master equation approach is used to model internal energy relaxation, but instead of solving the master equation directly, the underlying random process is simulated. Three different models are suggested, describing internal particle energies as continuous scalars or as a set of discrete levels. The proposed models are implemented in the well-known cubic Fokker-Planck model using the SPARTA particle simulation framework, and relaxation, expansion flow and shock flow test cases are investigated to demonstrate their performance.