The particle module in PICLas allows to easily implement and utilize different particle-based solvers such as the Particle in Cell, Direct Simulation Monte Carlo, Bhatnagar-Gross-Krook, and the Monte Carlo Collision methods. The solvers take advantage of the common particle localization and tracking algorithms as well as a common treatment of the boundary conditions. A schematic of a time step in PICLas is shown below.

#### Direct Simulation Monte Carlo

The Direct Simulation Monte Carlo (DSMC) method in PICLas for the simulation of non-equilibrium, high-enthalpy rarefied gas flows has a multitude of features including:

- 1D, 2D, axisymmetric (including a radial weighting) and 3D simulations
- Mesh independence with the on-the-fly octree-based mesh refinement and a nearest neighbour algorithm, see Pfeiffer et al. (2013)
- Broad range of available species from electrons to polyatomic molecules such as methane and carbon-dioxide, see Pfeiffer et al. (2016) and Nizenkov et al. (2017)
- Treatment of chemical reactions & ionization processes using the Arrhenius-based Total Collision Energy (TCE) model, the threshold-based Quantum-Kinetic (QK) model or the cross-section-based Monte Carlo Collision (MCC) model

Application areas of the DSMC method range from atmospheric entry and in-space propulsion to terrestrial applications such as micro-channel flows and vacuum pumps.

#### Bhatnagar-Gross-Krook

The Bhatnagar-Gross-Krook (BGK) approximation allows the efficient simulation of denser gas flows, where the DSMC method becomes computationally expensive. While the particle-based method in PICLas is continuously extended, key features have already been implemented:

- 2D, axisymmetric (including a radial weighting), and 3D simulations, see Pfeiffer et al. (2019)
- Single species simulations with diatomic and polyatomic molecules using quantized vibrational energy treatment, see Pfeiffer (2018)
- Simulation of gas mixtures with the multi-species modelling for atomic and diatomic species, see Pfeiffer et al. (2021)

The goal of the on-going development is to reach the same feature level as within the DSMC method to allow a bidirectional coupling of both methods for applications such as atmospheric entry and in-space propulsion. Coupled BGK-DSMC simulations of a non-reactive single species gas showed great promise in terms of computational time reduction, as shown in the nozzle expansion case.

#### Monte Carlo Collisions

The Monte Carlo Collision (MCC) algorithm offers a simpler way to model particle collisions and chemical reactions in PICLas. It utilizes experimentally measured or ab-initio calculated cross-section data to model the collision, excitation and reaction probabilities. For plasma simulations, it can be utilized under the assumption of a constant background gas, which is multiple orders of magnitude greater than the ionized species.

#### Particle in Cell

The Particle in Cell (PIC) method treats the electromagnetic interaction of a collisionless flow. It can be coupled with other particle-based methods such as DSMC or MCC to include collisional processes. More details on the field solver behind PICLas' PIC implementation can be found here.

More information about the underlying theory and modelling can be found here:

- Pfeiffer, M., Mirza, A., & Nizenkov, P. (2021). Multi-species modeling in the particle-based ellipsoidal statistical Bhatnagar–Gross–Krook method for monatomic gas species.
*Physics of Fluids*,**33**(3), 036106. - Pfeiffer, M., Mirza, A., & Nizenkov, P. (2019). Evaluation of particle-based continuum methods for a coupling with the direct simulation Monte Carlo method based on a nozzle expansion.
*Physics of Fluids*,**31**(7), 073601. - Pfeiffer, M. (2018). Extending the particle ellipsoidal statistical Bhatnagar-Gross-Krook method to diatomic molecules including quantized vibrational energies.
*Physics of Fluids*,**30**(11), 116103. - Nizenkov, P., Pfeiffer, M., Mirza, A., & Fasoulas, S. (2017). Modeling of chemical reactions between polyatomic molecules for atmospheric entry simulations with direct simulation Monte Carlo.
*Physics of Fluids*,**29**(7), 077104. - Pfeiffer, M., Nizenkov, P., Mirza, A., & Fasoulas, S. (2016). Direct simulation Monte Carlo modeling of relaxation processes in polyatomic gases.
*Physics of Fluids*,**28**(2), 027103. - Pfeiffer, M., Mirza, A., & Fasoulas, S. (2013). A grid-independent particle pairing strategy for DSMC.
*Journal of Computational Physics*,**246**, 28–36.