Coalescence

struct coagulation_run{FT<:AbstractFloat}

Struct initialising temp memory used for coagulation.

Input:

• Ns::Int : Number of superdroplets.

Fields:

• I::Vector{Int} : Vector of indexes to be shuffled for permutations.
• pαdt::Vector{FT} : Vector of coalescence probabilities for each pair.
• ϕ::Vector{FT} : Random numbers to be used in Monte Carlo coalescence.
• lowest_zero::Ref{Bool} : Reference to a boolean indicating if the lowest multiplicity is zero.
• deficit::Ref{FT} : Reference to a float representing the deficit in mass or volume.

coagulation_run_spatial{FT<:AbstractFloat}

struct for allocation related to coalescence in a spatially resolved simulation.

coalescence_timestep!(run::backend, scheme::scheme_type, droplets::droplet_attributes)

Perform a coalescence timestep for the given droplets using the Superdroplet Method (SDM) Shima et al. (2009) when the lowest multiplicity of superdroplets is less than 1, the largest superdroplet is split into two equal parts, as proposed by Dziekan and Pawlowska (ACP, 2017) https://doi.org/10.5194/acp-17-13509-2017

Arguments

• run::backend: Serial or Parallel
• scheme::schemetype: adaptive timestepping or none
• droplets::droplet_attributes: The superdroplets.

if dropletattributes1d, coagdata must be coagulationrun_spatial

adaptive_pαdt!(L::Vector{Tuple{Int,Int}}, droplets::droplet_attributes, coag_data::coagulation_run, t_left::Ref{FT}, kernel::Function, settings::coag_settings{FT}) where FT<:AbstractFloat

Map the probability function over the list of droplet pairs, L, using adaptive timestepping logic and update the coagulation data in place.

Arguments

• L::Vector{Tuple{Int,Int}}: List of droplet indices.
• droplets::droplet_attributes: Droplet attributes.
• coag_data::coagulation_run: Coagulation data.
• t_left::Ref{FT}: Timestep after adaptive substep.
• kernel::Function: Coalescence kernel function.
• settings::coag_settings{FT}: Coagulation settings.

compute_pαdt!(L::Vector{Tuple{Int,Int}}, droplets::droplet_attributes, coag_data::coagulation_run, kernel::Function, scale::FT,scalecoagsettings::coag_settings{FT}) where FT<:AbstractFloat

Map the probability function over the list of droplet pairs, L, and update the coagulation data in place.

Arguments

• L::Vector{Tuple{Int,Int}}: List of droplet indices to be considered for coalescence.
• droplets::droplet_attributes: Droplet attributes.
• coag_data::coagulation_run: Coagulation data.
• kernel::Function: Coalescence kernel function.
• coagsettings::coag_settings{FT}: Coagulation settings.

pair_Ps_adaptive!(α::Int, pair::Tuple{Int,Int}, droplets::droplet_attributes, coag_data::coagulation_run, t_max::Vector{FT})

This function calculates the coalescence probability for a given pair of droplets, using adaptive timestepping logic (Bartman et al. 2021). It takes the following arguments:

• α::Int: The index of the coalescence model.
• pair::Tuple{Int,Int}: The indices of the droplets in the pair.
• droplets::droplet_attributes: The attributes of the droplets.
• coag_data::coagulation_run: The coagulation run data.
• t_max::Vector{FT}: The maximum timestep allowed given multiple sampling.

sdm_update!(pair::Tuple{Int,Int}, α::Int, droplets::droplet_attributes, coag_data::coagulation_run)

Perform the SDM coalescence update for the superdroplets when a coalesence event is determined, updating the droplet attributes in place.

Arguments

• pair::Tuple{Int,Int}: The pair of droplets to be updated.
• α::Int: The index of the coalescence model.
• droplets::droplet_attributes: The droplet attributes.
• coag_data::coagulation_run: The coagulation data.

test_pairs!(scheme::backend, Ns::Int, L::Vector{Tuple{Int,Int}}, droplets::droplet_attributes, coag_data::coagulation_run)

Perform the SDM coalescence update for the superdroplets. Update the droplet attributes in place in case of coalescence event.

Arguments

• scheme::Union{Serial, Parallel}: The scheme to use for the update.
• Ns::Int: The number of superdroplets.
• L::Vector{Tuple{Int,Int}}: The list of droplet pairs.
• droplets::droplet_attributes: The droplet attributes.
• coag_data::coagulation_run: The coagulation data.

init_logarithmic(settings::coag_settings{FT}) where FT<:AbstractFloat

init_logarithmic initializes the superdroplets, using a logarithmically spaced droplet radius spectrum, initializing the multiplicities so that the water volume in the system forms an exponential distribution around the initial volume.

Arguments

• settings: Coagulation settings.

init_monodisperse(settings::coag_settings{FT}) where FT<:AbstractFloat

init_monodisperse initializes the superdroplets so that all droplets have the same attributes. Arguments

• settings: Coagulation settings.

inituniformsd(settings::coag_settings{FT}) where FT<:AbstractFloat

inituniformsd initializes the superdroplets, using an evenly spaced droplet radius spectrum, initializing the multiplicities so that the water volume in the system forms an exponential distribution around the initial volume.

Arguments

• settings: Coagulation settings.

init_ξ_const(settings::coag_settings{FT}) where FT<:AbstractFloat

initξconst initializes droplets based on the constant-multiplicity initialization method, using an exponential distribution around the initial volume of the droplets. The method is as described in Shima et al. (2009) https://doi.org/10.5194/acp-9-4491-2009

Arguments

• settings: Coagulation settings, type ::coag_settings.

" golovinSCE(x,x0,n0,b,time)

Analytic solution to the Smoluchowski Collection Equation using the Golovin (additive) kernel (Golovin, 1963).

Arguments

• x:: volume evaulated at
• x0:: initial volume
• n0:: initial number density
• b:: Golovin kernel coefficient
• time:: time at which to evaluate the solution

Note the use of the besselix function rather than besseli, to solve overflow issues. The exponential term is then modified to compensate.