4.11. Fokker-Planck Collision Operator
The implementation of the FP-based collision operator is based on the publications by [57] and [58]. It is a method, which allows the simulation of gas flows in the continuum and transitional regime, where the DSMC method is computationally too expensive. The collision integral is hereby approximated by a drift and diffusion process
where \(\mathbf{A}\) is the drift vector and \(\mathcal{D}\) the diffusion matrix.
The current implementation supports:
2 different methods: Cubic and Ellipsoidal Statistical (ES)
Single species, monatomic and polyatomic gases
Thermal non-equilibrium with rotational and vibrational excitation (continuous or quantized treatment)
2D/Axisymmetric simulations
Variable time step (adaption of the distribution according to the maximal relaxation factor and linear scaling)
Relevant publications of the developers:
Implementation of the cubic Fokker-Planck in PICLas [58]
Comparison of the cubic and ellipsoidal statistical Fokker-Planck [59]
Simulation of a nozzle expansion (including the pressure chamber) with ESBGK, ESFP and coupled ESBGK-DSMC, comparison to experimental measurements [60]
To enable the simulation with the FP module, the respective compiler setting has to be activated:
PICLAS_TIMEDISCMETHOD = FP-Flow
A parameter file and species initialization file is required, analogous to the DSMC setup. It is recommended to utilize a previous
DSMC parameter file to ensure a complete simulation setup. To enable the simulation with the FP methods, select the Fokker-Planck
method, cubic (=1
) and ES (=2
):
Particles-FP-CollModel = 2
The vibrational excitation can be controlled with the following flags, including the choice between continuous and quantized vibrational energy:
Particles-FP-DoVibRelaxation = T
Particles-FP-UseQuantVibEn = T
An octree cell refinement until the given number of particles is reached can be utilized, which corresponds to an equal refinement in all three directions (x,y,z):
Particles-FP-DoCellAdaptation = T
Particles-FP-MinPartsPerCell = 10
A coupled FP-DSMC simulation can be enabled, where the FP method will be utilized if the number density \([\text{m}^{-3}]\) is above a certain value:
Particles-CoupledFPDSMC = T
Particles-FP-DSMC-SwitchDens = 1E22
The flag Particles-DSMC-CalcQualityFactors
controls the output of quality factors such as mean/maximal relaxation factor (mean:
average over a cell, max: maximal value within the octree), max rotational relaxation factor, which are defined as
where \(\Delta t\) is the chosen time step and \(1/\tau\) the relaxation frequency. The time step should be chosen as such that the
relaxation factors are below unity. The FP_DSMC_Ratio
gives the percentage of the sampled time during which the FP model was utilized.
In a couple FP-DSMC simulation this variable indicates the boundary between FP and DSMC. However, a value below 1 can occur for
pure FP simulations due to low particle numbers, when an element is skipped. Additionally, the Prandtl number utilized by the ESFP
model is given.