A combined approach for the simulation of reactive, neutral, partially or fully ionized plasma flows is presented. This is realized in a code framework named “PICLas” for the approximate solution of the Boltzmann equation by particle based methods. PICLas combines the particle-in-cell method for the collisionless Vlasov–Maxwell system and the direct simulation Monte Carlo method for neutral reactive flows. Basic physical and mathematical modeling of both methods is addressed, and some application examples are presented in order to demonstrate the capabilities and the broad applicability of the solution strategy.

Over the past half century, a variety of computational fluid dynamics (CFD) methods and the direct simulation Monte Carlo (DSMC) method have been widely and successfully applied to the simulation of gas flows for the continuum and rarefied regime, respectively. However, they both encounter difficulties when dealing with multiscale gas flows in modern engineering problems, where the whole system is on the macroscopic scale but the nonequilibrium effects play an important role. In this paper, we review two particle-based strategies developed for the simulation of multiscale nonequilibrium gas flows, i.e., DSMC-CFD hybrid methods and multiscale particle methods. The principles, advantages, disadvantages, and applications for each method are described. The latest progress in the modelling of multiscale gas flows including the unified multiscale particle method proposed by the authors is presented.

Plasma flows with high Knudsen numbers cannot be treated with classic continuum methods, as represented for example by the Navier–Stokes or the magnetohydrodynamic equations. Instead, the more fundamental Boltzmann equation has to be solved, which is done here approximately by particle based methods that also allow for thermal and chemical non-equilibrium. The Particle-In-Cell method is used to treat the collisionless Vlasov–Maxwell system, while neutral reactive flows are treated by the Direct Simulation Monte Carlo method. In this article, a combined approach is presented that allows the simulation of reactive, partially or fully ionized plasma flows. Both particle methods are briefly outlined and the coupling and parallelization strategies are described. As an example, the results of a streamer discharge simulation are presented and discussed in order to demonstrate the capabilities of the coupled method.

The Bhatnagar-Gross-Krook (BGK) model and its extensions (ellipsoidal statistical BGK, Shakhov BGK, and unified BGK) are used in particle-based fluid dynamics and compared with the Direct Simulation Monte Carlo (DSMC) method. To this end, different methods are investigated that allow efficient sampling of the Shakhov and the unified target distribution functions. As a consequence, particle simulations based on the Shakhov BGK and unified BGK models are possible in an efficient way. Furthermore, different energy conservation schemes are tested for the BGK models. It is shown that the choice of the energy conservation scheme has a major impact on the quality of the results for each model. The models are verified with a Couette flow problem at different Knudsen numbers and wall velocities. Furthermore, the models are compared with the DSMC results of a hypersonic flow around a 70° blunted cone. It is shown that the unified BGK model is able to reproduce rarefied gas phenomena. Furthermore, it is shown that the difference in the reproduction of the shock structure is not significant between the ellipsoidal statistical BGK and Shakhov BGK models for the flow around a 70° blunted cone and significantly depends on the energy conservation method. The choice of the energy conservation method is especially crucial for the Shakhov model whereas the ellipsoidal statistical BGK model is much more robust concerning the energy conservation scheme. Additionally, a computational time study is performed to show the efficiency of BGK-based simulations for low Knudsen number flows compared with DSMC.

This paper investigates three different particle-based continuum methods, the ellipsoidal statistical Bhatnagar-Gross-Krook (ESBGK) and Fokker-Planck (ESFP) methods and the Low Diffusion (LD) method, for a coupling with the direct simulation Monte Carlo (DSMC) method. After a short description of the methods and their implementation, including the coupling concept for the LD-DSMC, simulation results of a nozzle expansion are compared with available experimental measurements and a DSMC simulation. Excellent agreement between ESBGK, ESFP, and DSMC can be observed in the throat of the nozzle, while the LD method fails to predict the correct velocity, temperature, and density profile. Further downstream, only the DSMC and the coupled ESBGK/ESFP-DSMC simulations are able to reproduce the measured rotational temperature profiles. A performance comparison shows the possible computational savings of a coupled ESBGK/ESFP-DSMC simulation, where a speedup of four orders of magnitude can be observed compared to a regular DSMC simulation.