4.5. Particle Initialization & Emission

The RAM to store the particles is dynamically allocated. However, it is possible to restrict the number of particles per MPI process by setting

Part-MaxParticleNumber=1000000

New memory is allocated in separate chunks because allocating memory for the particle data and copying it to the new memory area is expensive. The chunksize is relative to the particles used and can be set with

Part-MaxPartNumIncrease=0.1

A higher value increases the amount of unnecessary RAM allocated to particles, while a lower value increases the number of memory adjustment operations. The optimal trade-off depends on the simulation and the machine, but it only affects the performance of the simulations, not the quality of the results.

The following section gives an overview of the available options regarding the definition of species and particle initialization and emission. Simulation particles can be inserted initially within the computational domain and/or emitted at every time step. First of all, the number of species is defined by

Part-nSpecies=1

Regardless whether a standalone PIC, DSMC, or a coupled simulation is performed, the atomic mass [kg], the charge [C] and the weighting factor $w$ [-], sometimes referred to as macro-particle factor (MPF), are required for each species.

Part-Species1-MassIC=5.31352E-26
Part-Species1-ChargeIC=0.0
Part-Species1-MacroParticleFactor=5E2

Species that are not part of the initialization or emission but might occur as a result of e.g. chemical reactions should also be defined with these parameters.

Due to the often repetitive definitions, the default value for a given parameter can be set using the wildcard $. Different values for individual parameters can be specified by explicitly specifying the numbered parameter, irrespective of the ordering in the parameter file.

Part-Species1-Init1-VeloIC = 1.
Part-Species$-Init$-VeloIC = 2.

Due to runtime considerations, the evaluation of the wildcard character is performed from left to right. Thus, a parameter like Part-Species1-Init$-VeloIC will not work.

Different velocity distributions are available for the initialization/emission of particles.

Distribution	Description
maxwell	Maxwell-Boltzmann distribution
maxwell_lpn	Maxwell-Boltzmann distribution for low particle numbers
WIP	WORK IN PROGRESS

Some emission types allow the usage of an emission-specific particle weighting factor. The default weighting factor given by Part-Species1-MacroParticleFactor can be overwritten by supplying a different one for each initialization, for which the variable weighting factor (or variable macro-particle factor vMPF) model must be activated

Part-vMPF = T
Part-Species1-Init1-MacroParticleFactor = 1e4

4.5.1. Initialization

At the beginning of a simulation, particles can be inserted using different initialization routines. Initialization regions are defined per species and can overlap. First, the number of initialization conditions/regions has to be defined

Part-Species1-nInits = 1

The type of the region is defined by the following parameter

Part-Species1-Init1-SpaceIC = cell_local

Different SpaceIC are available and an overview is given in the table below.

Distribution	Description	Reference
cell_local	Particles are inserted in every cell at a constant number density	Section Cell local
disc	Particles are inserted on a circular disc	Section Circular Disc
cuboid	Particles are inserted in the given cuboid volume at a constant number density	Section Cuboid
cylinder	Particles are inserted in the given cylinder volume at a constant number density	Section Cylinder
sphere	Particles are inserted in the given sphere volume at a constant number density	Section Sphere
photon_cylinder	Ionization of a background gas through photon impact (cylinder distribution)	Section Photo-ionization
photon_SEE_disc	Secondary electron emission through photon impact (disk distribution)	Section Photo-ionization
photon_honeycomb	Ionization of a background gas through photon impact (honeycomb distribution)	Section Photo-ionization
photon_SEE_honeycomb	Secondary electron emission through photon impact (honeycomb distribution)	Section Photo-ionization
photon_rectangle	Ionization of a background gas through photon impact (rectangular distribution)	Section Photo-ionization
photon_SEE_rectangle	Secondary electron emission through photon impact (rectangular distribution)	Section Photo-ionization
EmissionDistribution	Initial only ($t=0$) field-based ($n, T, v$) particle distribution from .h5	Section Emission Distribution

Common parameters required for most of the insertion routines are given below. The drift velocity is defined by the direction vector VeloVecIC, which is a unit vector, and a velocity magnitude [m/s]. The thermal velocity of particle is determined based on the defined velocity distribution and the given translation temperature MWTemperatureIC [K]. Finally, the ‘real’ number density is defined by PartDensity [1/m$^3$], from which the actual number of simulation particles will be determined (depending on the chosen weighting factor).

Part-Species1-Init1-VeloIC=1500
Part-Species1-Init1-VeloVecIC=(/-1.0,0.0,0.0/)
Part-Species1-Init1-velocityDistribution=maxwell_lpn
Part-Species1-Init1-MWTemperatureIC=300.
Part-Species1-Init1-PartDensity=1E20

In the case of molecules, the rotational and vibrational temperature [K] have to be defined. If electronic excitation is considered, the electronic temperature [K] has to be defined

Part-Species1-Init1-TempRot=300.
Part-Species1-Init1-TempVib=300.
Part-Species1-Init1-TempElec=300.

The parameters given so far are sufficient to define an initialization region for a molecular species using the cell_local option. Additional options required for other insertion regions are described in the following.

4.5.1.1. Cell local

Additional options are available to limit the local emission to certain limits in each dimension (x,y,z) as defined by:

Part-Species1-Init1-MinimalLocation       = (/ -1.0, -1.0, -999. /)
Part-Species1-Init1-MaximalLocation       = (/  1.0,  1.0,  999. /)

To limit the insertion only to a specific dimension, simply provide a sufficiently large number for the other dimensions. This approach can also be utilized for 2D and axisymmetric simulations.

When using a variable particle weighting as described in Section Variable Particle Weighting, the variable Part-Species1-vMPFSplitThreshold will be utilized as the target number of particles per cell during the insertion and the weighting factor will be determined from the given number density and cell volume.

4.5.1.2. Circular Disc

To define the circular disc the following parameters are required:

Part-Species1-Init1-SpaceIC               = disc
Part-Species1-Init1-RadiusIC              = 1
Part-Species1-Init1-BasePointIC           = (/ 0.0, 0.0, 0.0 /)
Part-Species1-Init1-BaseVector1IC         = (/ 1.0, 0.0, 0.0 /)
Part-Species1-Init1-BaseVector2IC         = (/ 0.0, 1.0, 0.0 /)
Part-Species1-Init1-NormalIC              = (/ 0.0, 0.0, 1.0 /)

The first and second base vector span a plane, where a circle with the given radius will be defined at the base point.

4.5.1.3. Cuboid

To define the cuboid the following parameters are required:

Part-Species1-Init1-SpaceIC               = cuboid
Part-Species1-Init1-RadiusIC              = 1
Part-Species1-Init1-CuboidHeightIC        = 1
Part-Species1-Init1-BasePointIC           = (/ 0.0, 0.0, 0.0 /)
Part-Species1-Init1-BaseVector1IC         = (/ 1.0, 0.0, 0.0 /)
Part-Species1-Init1-BaseVector2IC         = (/ 0.0, 1.0, 0.0 /)
Part-Species1-Init1-NormalIC              = (/ 0.0, 0.0, 1.0 /)

The first and second base vector span a side of the cuboid, and then its extruded in the normal direction up to the cuboid height.

For symmetric simulations Part-Species1-Init1-BaseVector2IC is set in direction of the symmetry (/ 0.0, 0.0, 1.0 /)

4.5.1.4. Cylinder

To define the cylinder the following parameters are required:

Part-Species1-Init1-SpaceIC               = cylinder
Part-Species1-Init1-RadiusIC              = 1
Part-Species1-Init1-CylinderHeightIC      = 1
Part-Species1-Init1-BasePointIC           = (/ 0.0, 0.0, 0.0 /)
Part-Species1-Init1-BaseVector1IC         = (/ 1.0, 0.0, 0.0 /)
Part-Species1-Init1-BaseVector2IC         = (/ 0.0, 1.0, 0.0 /)
Part-Species1-Init1-NormalIC              = (/ 0.0, 0.0, 1.0 /)

The first and second base vector span a plane, where a circle with the given radius will be defined at the base point and then extruded in the normal direction up to the cylinder height.

For symmetric simulations Part-Species1-Init1-BaseVector2IC is set in direction of the symmetry (/ 0.0, 1.0, 0.0 /) for 2D planar simulations, and (/ 0.0, 0.0, 1.0 /) for axisymmetric ones.

4.5.1.5. Sphere

To define the cuboid the following parameters are required:

Part-Species1-Init1-SpaceIC               = sphere
Part-Species1-Init1-RadiusIC              = 1
Part-Species1-Init1-BasePointIC           = (/ 0.0, 0.0, 0.0 /)
Part-Species1-Init1-NormalIC              = (/ 0.0, 0.0, 1.0 /)

4.5.1.6. Photo-ionization

A special case is the ionization of a background gas through photon impact, modelling a light pulse. The volume affected by the light pulse is approximated by a cylinder (or honeycomb/rectangle), which is defined as described in Section Cylinder. Additionally, the SpaceIC has to be adapted and additional parameters are required:

Part-Species1-Init1-SpaceIC       = photon_cylinder ! or photon_honeycomb, or photon_rectangle
Part-Species1-Init1-PulseDuration = 1               ! [s]
Part-Species1-Init1-WaistRadius   = 1E-6            ! [m]
Part-Species1-Init1-WaveLength    = 1E-9            ! [m]
Part-Species1-Init1-NbrOfPulses   = 1               ! [-], default = 1

The pulse duration and waist radius are utilized to define the spatial and temporal Gaussian profile of the intensity. The number of pulses allows to consider multiple light pulses within a single simulation. To define the intensity of the light pulse, either the average pulse power (energy of a single pulse times repetition rate), the pulse energy or the intensity amplitude have to be provided.

Part-Species1-Init1-Power                   = 1         ! [W]
Part-Species1-Init1-RepetitionRate          = 1         ! [Hz]
! or
Part-Species1-Init1-Energy                  = 1         ! [J]
! or
Part-Species1-Init1-IntensityAmplitude      = 1         ! [W/m^2]

The intensity can be scaled with an additional factor to account for example for reflection or other effects:

Part-Species1-Init1-EffectiveIntensityFactor    = 1         ! [-]

It should be noted that this initialization should be done with a particle species (i.e. not the background gas species) that is also a product of the ionization reaction. The ionization reactions are defined as described in Section Chemistry & Ionization by

DSMC-NumOfReactions = 1
DSMC-Reaction1-ReactionType = phIon
DSMC-Reaction1-Reactants    = (/3,0,0/)
DSMC-Reaction1-Products     = (/1,2,0/)
DSMC-Reaction1-CrossSection = 4.84E-24      ! [m^2]

The probability that an ionization event occurs is determined based on the given cross-section, which is usually given for a certain wave length/photon energy. It should be noted that the background gas species should be given as the sole reactant and electrons should be defined as the first and/or second product. Electrons will be emitted perpendicular to the light path defined by the cylinder axis according to a cosine squared distribution.

Finally, the secondary electron emission through the impinging light pulse on a surface can also be modelled by an additional insertion region (e.g. as an extra initialization for the same species). Additionally to the definition of the light pulse as described above (pulse duration, waist radius, wave length, number of pulses, and power/energy/intensity), the following parameters have to be set

Part-Species1-Init2-SpaceIC               = photon_SEE_disc     ! or photon_SEE_honeycomb, or photon_SEE_rectangle
Part-Species1-Init2-velocityDistribution  = photon_SEE_energy
Part-Species1-Init2-YieldSEE              = 0.1                 ! [-]
Part-Species1-Init2-WorkFunctionSEE       = 2                   ! [eV]

The emission area is defined as a disc by the parameters introduced in Section Circular Disc. The yield controls how many electrons are emitted per photon impact and their velocity distribution is defined by the work function. The scaling factor defined by EffectiveIntensityFactor is not applied to this surface emission. Both emission regions can be sped-up if the actual computational domain corresponds only to a quarter of the cylinder:

Part-Species1-Init1-FirstQuadrantOnly       = T
Part-Species1-Init2-FirstQuadrantOnly       = T

4.5.1.7. Emission Distribution

To initialize a pre-defined distribution, e.g., from the output of a field-based or continuum-based solver, a particle distribution can be created from a .h5 file that contains $n, T, v_{r}$ and $v_{z}$ (particle number density, temperature and velocity in 2D cylindrical coordinates). This data needs to be supplied in a specific format and a different array for each species that is to be initialized in such a way is required. This emission option is selected via

! Define the name of the data file
Part-EmissionDistributionFileName = reggie-linear-rot-symmetry-species-init.h5

! OPTIONAL: Polynomial degree for particle emission in each element
Part-EmissionDistributionN = 1

! For each species, the following information is required
Part-Species1-nInits   = 1
Part-Species1-Init1-SpaceIC                  = EmissionDistribution
Part-Species1-Init1-EmissionDistributionName = HeIon

where Part-EmissionDistributionFileName defines the .h5 data file that contains the data, Part-EmissionDistributionN is an optional parameter for tuning the quality of the distribution within each element. It defines the polynomial degree for the particle emission in each element. The default value is 2(N+1) with N being the polynomial degree of the solution. The parameter Part-Species1-Init1-SpaceIC activates this specific emission type and Part-Species1-Init1-EmissionDistributionName is the name of the container in the .h5 file that yields the data for each species.

An example setup is given in the regression check directory under ./regressioncheck/CHE_PIC_maxwell_RK4/2D_variable_particle_init_n_T_v. The example uses 2D data defined in cylindrical coordinates for the velocity vector $v=v(r,z)$, which will be transformed to Cartesian coordinates in piclas.

The .h5 file reggie-linear-rot-symmetry-species-init.h5 contains the following information: Attributes that define the index of the coordinates and the properties

T   4
n   3
r   1
vr  5
vz  6
z   2

and two array container, one for each species labelled HeIon and electron for singly charged Helium ions and electrons. These names must be used in the parameter input file. Each of these containers must provide the data in a $m \times n$ array and must be equidistant in each coordinate direction. The electron data begins with the following data

0   5.0     NaN      NaN        NaN        NaN
0   7.0  2.4E17  10000.0  1000000.0  1000000.0
0   9.0  2.4E17  10000.0  1000000.0  1000000.0
0  11.0  2.4E17  10000.0  1000000.0  1000000.0
0  13.0  2.4E17  10000.0  1000000.0  1000000.0
...
...

and is allowed to contain NaN values, because the original data might be projected onto a equidistant Cartesian grid from a unstructured and non-rectangular mesh. These NaN values will automatically be replaced with zeros during read-in of the data. The original 2D data (equidistant mesh) must be unrolled into a 1D structure with one data point per row. As can be seen from the dataset above, the first column containing the $r$-coordinates is the outer loop and the $z$-coordinates in the second column represent the inner loop in this logic. Note that the temperature (translational, vibrational and electronic) of ions and atoms/molecules will be initialized with $300$ K. This will be changed in a future release. At the moment, only the electron temperature will be considered.

4.5.1.8. Neutralization Boundaries (neutral outflow condition)

There are different methods implemented to neutralize a charged particle flow, e.g., as encountered when simulation electric propulsion systems. Currently all methods require a specific geometry to function properly. For more details, see the regression tests under regressioncheck/NIG_PIC_poisson_Boris-Leapfrog. The following table lists the SpaceIC emission types

Distribution	Description
2D_landmark_neutralization	Charoy 2019 2D PIC benchmark, electrons are injected with 10 eV at the cathode if the anode current is negative
2D_Liu2010_neutralization	Liu 2010 2D PIC benchmark, electrons are injected at the cathode if the cathode current is negative
2D_Liu2010_neutralization_Szabo	Liu 2010 2D PIC benchmark, electrons are injected in the first cell layer at the cathode if the net charge in these elements is positive
3D_Liu2010_neutralization	Liu 2010 3D PIC benchmark, electrons are injected at the cathode if the cathode current is negative
3D_Liu2010_neutralization_Szabo	Liu 2010 3D PIC benchmark, electrons are injected in the first cell layer at the cathode if the net charge in these elements is positive

For the XD_Liu2010_neutralization emission, a constant emitted electron temperature is defined via

Part-SpeciesX-InitX-MWTemperatureIC = 5.80E+04 ! 5.0 eV

whereas it is also possible to use a variable temperature, in which case the global (bulk) electron temperature is used, by setting

Part-SpeciesX-InitX-velocityDistribution = 2D_Liu2010_neutralization

for the 2D setup and

Part-SpeciesX-InitX-velocityDistribution = 3D_Liu2010_neutralization

for the 3D setup. The bulk electron temperature is determined automatically and output to PartAnalyze.csv as XXX-BulkElectronTemp-[K] to track this value over time.

4.5.1.9. Polychromatic Photo-ionization

The volumetric photo-ionization can consider multiple wavelengths (polychromatic spectrum) and/or energy-dependent cross-section data. The corresponding ionization reactions are defined described in Section Chemistry & Ionization by

DSMC-NumOfReactions = 1
DSMC-Reaction1-ReactionType = phIonXsec
DSMC-Reaction1-Reactants    = (/3,0,0/)
DSMC-Reaction1-Products     = (/1,2,0/)

where the reaction type phIonXsec refers to energy-dependent cross-section data for photoionization reactions. In this example, species 3 refers to H2 molecules, species 1 and 2 to electrons and H2+ ions respectively. The cross sections and photon energy spectrum must be supplied via

Particles-CollXSec-Database = XSec_Database_H2_Photoionization.h5

that must contain the data in the following form

XSec_Database_H2_Photoionization.h5
  - H2-photon (Group)
    - REACTION (Group)
      - H2Ion1-electron (Dataset)
    - SPECTRUM (Group)
      - H2-photon (Dataset)

where HIon1-electron (Dataset) contains the tabulated cross-sections and H2-photon (Dataset) contains the tabulated photon energies and energy fractions (the fractions must add up to unity). In principle, the spectrum can contain only 1 single photon energy (corresponding to a single wavelength) that contains all the energy, hence, the table contains the energy in eV and the number 1. (100% of the energy).

4.5.1.10. Initial Ionization

A neutral DSMC simulation can be converted into a PIC simulation (actually any simulation result state file *_State_*.h5) by specifying the number of species, their species ID and the desired ionization degree.

! Initial Ionization
Part-DoInitialIonization       = T       ! ON/OFF Switch
InitialIonizationSpecies       = 2       ! Total number of ions/neutrals that are to be created
InitialIonizationSpeciesID     = (/1,3/) ! Species 1 und 3 will be created (all read-in particles will be converted).
                                         ! Electrons do not have to be defined here as they are found automatically.
InitialIonizationChargeAverage = 0.1     ! 10% ionization degree

The switch Part-DoInitialIonization=T must be deactivated after the ionization was successful in order to prevent multiple ionization events of subsequent state files when further restarts are performed. Note that all particle species that are found in the state file are considered for ionization, i.e., that the number of species (InitialIonizationSpecies) is only required for all non-electron species that need to be present after the initial ionization has been performed. In this example, the state file contains solely particles of species 1 (neutral atoms or molecules). These particles are converted to 10 % species 3 (ions) and 90 percent species 1 (the original neutral particles), in addition to electrons which are found automatically by comparing the charge of the species (in this example species index 2). For each ion an electron is created to maintain charge neutrality. The ionization degree (InitialIonizationChargeAverage) should be a number between 0 and 1.

4.5.2. Surface Flux

A surface flux enables the emission of particles at a boundary in order to simulate, e.g. a free-stream. They are defined species-specifically and can overlap. First, the number of surface fluxes has to be given

Part-Species1-nSurfaceFluxBCs=1

The surface flux is mapped to a certain boundary by giving its boundary number (e.g. BC=1 corresponds to the previously defined boundary BC_OPEN)

Part-Species1-Surfaceflux1-BC=1

The remaining parameters such as flow velocity, temperature and number density are given analogously to the initial particle insertion presented in Section Initialization. An example to define the surface flux for a diatomic species is given below

Part-Species1-Surfaceflux1-VeloIC=1500
Part-Species1-Surfaceflux1-VeloVecIC=(/-1.0,0.0,0.0/)
Part-Species1-Surfaceflux1-velocityDistribution=maxwell_lpn
Part-Species1-Surfaceflux1-MWTemperatureIC=300.
Part-Species1-Surfaceflux1-PartDensity=1E20
Part-Species1-Surfaceflux1-TempRot=300.
Part-Species1-Surfaceflux1-TempVib=300.
Part-Species1-Surfaceflux1-TempElec=300.

4.5.2.1. Emission Current & Mass Flow

Instead of the particle number density PartDensity, an emission current $I$ [A] (e.g. to model a thermionic emission) or a mass flow $\dot{m}$ [kg/s] (e.g. to model outgassing) can be given:

Part-Species1-Surfaceflux1-EmissionCurrent=2
! or
Part-Species1-Surfaceflux1-Massflow=1e-11

In this case, the number of simulation particles to be inserted each time step $\Delta t$ is determined directly from the rate. The emission current only allows charged species and determines the number of particles according to the charge. The velocity magnitude can be zero (per default) or a defined value (through VeloIC and VeloVecIC). The respective boundary can be open or reflective. An example can be found in the regression test regressioncheck/CHE_DSMC/SurfFlux_Tria_CurrentMassflow For subsonic boundary conditions, where the velocity at the boundary is unknown, refer to Section Adaptive/Subsonic Boundaries.

4.5.2.2. Thermionic Emission (including Schottky effect)

The Richardson-Dushman equation including the Schottky effect is implemented and can be enabled to model thermionic emission

\[j = A^* T_{\mathrm{w}} ^2 \exp\left(-\frac{W^*}{k_{\mathrm{B}} T_{\mathrm{w}}}\right), \]

where the work function $W^*$ is defined by

\[W^* = W - \Delta W \qquad \Delta W = \sqrt{\frac{q_{\mathrm{e}}^3 |\mathbf{E}|}{4\pi\epsilon_0}}.\]

The magnitude of the electric field strength $|\mathbf{E}|$ is calculated with the average value of the interpolation points at the boundary. The material-specific properties such as the work function $W$ [eV] and the (modified) Richardson constant $A^*$ [A/cm²/K²] have to be provided as input. In addition to the surface flux parameters, a wall temperature $T_{\mathrm{w}}$ for the respective boundary has to be defined (as shown in Section Boundary Conditions - Particle Solver)

Part-Boundary1-WallTemp = 2000.
Part-Species1-Surfaceflux1-ThermionicEmission                    = TRUE
Part-Species1-Surfaceflux1-ThermionicEmission-SchottkyEffect     = TRUE
Part-Species1-Surfaceflux1-ThermionicEmission-WorkFunction       = 3
Part-Species1-Surfaceflux1-ThermionicEmission-RichardsonConstant = 120

The provided temperature for the surface flux of the species determines the energy of emitted particles. While the thermionic emission can be enabled for PIC as well as DSMC simulations, the addition of the Schottky effect requires a field solver. An overview of the limitations of this modelling regarding the applied field strength, wall temperature and/or material is given by Ref. [22] and Ref. [23]. An example can be found in the regression test regressioncheck/CHE_poisson/SurfFlux_ThermionicEmission_Schottky.

4.5.2.3. Circular Inflow

The emission of particles from a surface flux can be limited to the area within a circle, ring or circle cut-out. The respective boundary has to coincide or be parallel to the xy-, xz, or yz-planes. This allows to define inflow boundaries without specifically meshing the geometrical feature, e.g. small orifices. The feature can be enabled per species and surface flux

Part-Species1-Surfaceflux1-CircularInflow = TRUE

The normal direction of the respective boundary has to be defined by

Part-Species1-Surfaceflux1-axialDir = 1

Finally, the origin of the circle/ring on the surface and the radius have to be given. In the case of a ring, a maximal and minimal radius is required (-rmax and -rmin, respectively), whereas for a circle only the input of maximal radius and for the circle cut-out only the minimal radius is sufficient.

Part-Species1-Surfaceflux1-origin   = (/5e-6,5e-6/)
Part-Species1-Surfaceflux1-rmax     = 2.5e-6
Part-Species1-Surfaceflux1-rmin     = 1e-6

The absolute coordinates are defined as follows for the respective normal direction.

Normal Direction	Coordinates
x (=1)	(y,z)
y (=2)	(z,x)
z (=3)	(x,y)

Multiple circular inflows can be defined on a single boundary through multiple surface fluxes, e.g. to enable the simulation of multiple inlets on a chamber wall. Circular inflows are also supported with axisymmetric simulations, under the assumptions that the chosen surface is in the yz-plane (and thus has a normal direction in x) and the minimal and maximum radii are in the positive y-direction. Examples are given as part of the regression tests in regressioncheck/CHE_DSMC/SurfFlux_Tria_CircularInflow_Circle, SurfFlux_Tria_CircularInflow_CircleCutout and SurfFlux_Tria_CircularInflow_Ring.

4.5.2.4. Adaptive/Subsonic Boundaries

Different adaptive boundaries can be defined as a part of a surface flux to model subsonic in- and outflows, where the emission is adapted based on the prevalent conditions at the boundary. The modelling is based on the publications by Ref. [24] and Ref. [12].

Part-Species1-Surfaceflux1-Adaptive = TRUE
Part-Species1-Surfaceflux1-Adaptive-Type = 1

An overview over the available types is given below.

Type=1: Constant static pressure and temperature inlet, defined as Type 1 in Ref. [24]
Type=2: Constant static pressure outlet, defined as Type 1 in Ref. [24]
Type=3: Constant mass flow and temperature inlet, where the given mass flow and sampled velocity are used to determine the number of particles for the surface flux. It requires the BC to be defined as open. Defined as Type 2 in Ref. [24]
Type=4: Constant mass flow inlet and temperature inlet, where number of particles to be inserted is determined directly from the mass flow and the number of particles leaving the domain, $N_{\mathrm{in}}=N_{\dot{m}} + N_{\mathrm{out}}$. Defined as cf_3 in Ref. [12]

Depending of the type of the chosen boundary type either the mass flow [kg/s] or the static pressure [Pa] have to be given

Part-Species1-Surfaceflux1-Adaptive-Massflow = 1.00E-14
Part-Species1-Surfaceflux1-Adaptive-Pressure = 10

The adaptive boundaries require the sampling of macroscopic properties such as flow velocity at the boundary. To compensate for the statistical fluctuations, three possible sampling approaches are available. The first approach uses a relaxation factor $f_{\mathrm{relax}}$, where the current value of the sampled variable $v^{n}$ is updated according to

\[v^{n}= (1-f_{\mathrm{relax}})\,v^{n-1} + f_{\mathrm{relax}} v^{\mathrm{samp}} \]

The relaxation factor $f_{\mathrm{relax}}$ is defined by

AdaptiveBC-RelaxationFactor = 0.001

The second and third approach allows to sample over a certain number of iterations. If the truncated running average option is enabled, the macroscopic properties will be continuously updated while the oldest sample will be replaced with the most recent. If the truncated running average option is disabled, the macroscopic properties will be only updated every given number of iterations, and the complete sample will be resetted afterwads. If a number of iterations is given, it will be used instead of the first approach with the relaxation factor.

AdaptiveBC-SamplingIteration      = 100
AdaptiveBC-TruncateRunningAverage = T       ! DEFAULT: F

The adaptive particle emission can be combined with the circular inflow feature. In this context when the area of the actual emission circle/ring is very small, it is preferable to utilize the Type=4 constant mass flow condition. Type=3 assumes an open boundary and accounts for particles leaving the domain through that boundary already when determining the number of particles to be inserted. As a result, this method tends to over predict the given mass flow, when the emission area is very small and large sample size would be required to have enough particles that leave the domain through the emission area. For the Type=4 method, the actual number of particles leaving the domain through the circular inflow is counted and the mass flow adapted accordingly, thus the correct mass flow can be reproduced.

Additionally, the Type=4 method can be utilized in combination with a reflective boundary condition to model diffusion and leakage (e.g. in vacuum tanks) based on a diffusion rate $Q$ [Pa m$^3$ s$^{-1}$]. The input mass flow [kg s$^{-1}$] for the simulation is then determined by

\[\dot{m} = \frac{QM}{1000RT},\]

where $R=8.314$ J mol$^{-1}$K$^{-1}$ is the gas constant, $M$ the molar mass in [g mol$^{-1}$] and $T$ is the gas temperature [K]. It should be noted that while multiple adaptive boundaries are possible, adjacent boundaries that share a mesh element should be avoided or treated carefully. Examples are given as part of the regression tests in regressioncheck/CHE_DSMC/SurfFlux_Tria_Adaptive_ConstMassflow and SurfFlux_Tria_Adaptive_ConstPressure.

4.5.2.5. Verification

To verify the resulting current [A], mass flow rate [kg s$^{-1}$] or the pressure at an adaptive surface flux [Pa], the following option can be enabled

CalcSurfFluxInfo = T

This will output a species-specific rate and/or the average pressure in the adjacent cells (in case of an adaptive/subsonic BC) for each surface flux condition in the PartAnalyze.csv. It gives the current values for the time step. For the former, positive values correspond to a net flux into the domain and negative values vice versa.

4.5.2.6. Missing descriptions

ReduceNoise, DoForceFreeSurfaceFlux

DoPoissonRounding: [25]

AcceptReject, ARM_DmaxSampleN: [26]