Collision algorithms

Merzbild.jl implements several algorithms for modelling binary collisions: either directly or via the Fokker-Planck approach. All of them operate on the particles of a single grid cell, using the ParticleIndexerArray to access the particles of the relevant species. The variable-weight NTC variants split particles when the collision partners have unequal weights; the equal-weight variant skips these checks for performance.

Overview

Elastic scattering models

The DSMC and SWPM routines listed above support several models of elastic scattering, which define both the total collision cross-section $\sigma(g)$ (and thus the collision probability) and the angular scattering law (and thus the post-collisional velocities):

The model is fixed for a species pair and is stored in the pair's Interaction instance as a parameter of the Merzbild.ScatteringModel enum type. It is set by the optional model key of the pair's entry in the interaction data TOML file, defaulting to "VHS" if the key is absent:

["Ar,Ar"]
model = "VSS"
vhs_d = 4.11e-10
vhs_o = 0.81
vhs_Tref = 273.0
vss_alpha = 1.40

The VSS model requires the additional vss_alpha key; a bundled interaction data file using it is vss.toml (see MERZBILD_DATA_PATH). Since the VSS model modifies the angular scattering law but not the total cross-section, the reference viscosity of a VSS interaction is corrected by the factor $(\alpha + 1)(\alpha + 2)/(6\alpha)$; $\alpha = 1$ recovers isotropic scattering, and the VSS model then coincides with the VHS model.

A hard sphere gas is a special case of the VHS model, obtained by setting $\omega = 1/2$ in the interaction data file: the cross-section is then the constant $\pi d^2$.

The collision routines resolve the model of the species pair once per call, and are then compiled for that single model, so that no branching on the model, no dynamic dispatch and no allocations are left in the collision loop itself. The model can also be passed explicitly as the second positional argument (e.g. ntc!(rng, VSS(), collision_factors, ...)), which overrides the model stored in the Interaction instance. The dispatch is on singleton subtypes of the AbstractScatteringModel type via use of the Merzbild.@scattering_barrier macro that maps the scattering model enums to the singletons (via Merzbild.SCATTERING_MODEL_TAGS).

DSMC collisions

The No-Time-Counter (NTC) algorithm is the default DSMC collision routine. Four variants are available:

• ntc_equal_weight! — single-species collisions assuming all particles share the same computational weight; no weight checks or particle splitting are performed. This is the classic NTC scheme of Bird (1994).
• ntc_equal_weight! (two-species method) — collisions between particles of two different species with equal computational weights.
• ntc! — single-species collisions for variable-weight particles. When the collision partners' weights differ by more than dw_tol, particle splitting is used to conserve mass, momentum, and energy, following the variable-weight NTC approach of Schmidt and Rutland (2000).
• ntc! (two-species method) — collisions between particles of two different species, again supporting variable weights and particle splitting.

SWPM

swpm! implements the Stochastic Weighted Particle Method of Rjasanow and Wagner (2005) for single-species, variable-weight collisions. During a collision of particles with weights $w_i$, $w_j$, the weights are depleted by $\min(w_i, w_j) / (1+G)$, where $G \geq 0$ is a user-defined parameter controlling the weight-transfer function.

Fokker–Planck

fp_linear! models single-species elastic collisions using a linear Fokker–Planck approximation instead of resolving individual binary collisions, following the model of Gorji, Torrilhon, and Jenny (2011).

Electron–neutral collisions

For plasma simulations, dedicated NTC routines model electron–neutral elastic scattering together with electron-impact ionization, using tabulated cross-sections stored in an ElectronNeutralInteractions instance:

• ntc_n_e! — electron–neutral elastic scattering and electron-impact ionization without event splitting.
• ntc_n_e_es! — the same processes modelled with the event-splitting method of Oblapenko et al. (2022), which reduces statistical noise by splitting collision outcomes rather than sampling a single outcome per pair.

Because the electron–neutral cross-sections vary strongly with collision energy, the value of $(\sigma g w)_{max}$ needed by the NTC algorithm can be estimated stochastically with estimate_sigma_g_w_max_ntc_n_e! before performing the collisions.