PySDM

PySDM is a package for simulating the dynamics of population of particles. It is intended to serve as a building block for simulation systems modelling fluid flows involving a dispersed phase, with PySDM being responsible for representation of the dispersed phase. Currently, the development is focused on atmospheric cloud physics applications, in particular on modelling the dynamics of particles immersed in moist air using the particle-based (a.k.a. super-droplet) approach to represent aerosol/cloud/rain microphysics. The package core is a Pythonic high-performance implementation of the Super-Droplet Method (SDM) Monte-Carlo algorithm for representing collisional growth (Shima et al. 2009), hence the name.

PySDM has two alternative parallel number-crunching backends available: multi-threaded CPU backend based on Numba and GPU-resident backend built on top of ThrustRTC. The Numba backend named CPU is the default, and features multi-threaded parallelism for multi-core CPUs. It uses the just-in-time compilation technique based on the LLVM infrastructure. The ThrustRTC backend named GPU offers GPU-resident operation of PySDM leveraging the SIMT parallelisation model. Using the GPU backend requires nVidia hardware and CUDA driver.

For an overview paper on PySDM v1 (and the preferred item to cite if using PySDM), see Bartman et al. 2021 arXiv e-print (submitted to JOSS). For a list of talks and other materials on PySDM, see the project wiki.

Dependencies and Installation

PySDM dependencies are: Numpy, Numba, SciPy, Pint, chempy, ThrustRTC and CURandRTC.

To install PySDM using pip, use: pip install git+https://github.com/atmos-cloud-sim-uj/PySDM.git.

For development purposes, we suggest cloning the repository and installing it using pip -e. Test-time dependencies are listed in the requirements.txt file.

PySDM examples listed below are hosted in a separate repository and constitute a separate PySDM_examples Python package. The examples have additional dependencies listed in PySDM_examples package setup.py file. Running the examples requires the the PySDM_examples package to be installed (or within PYTHONPATH). Since the examples package includes Jupyter notebooks, the suggested install and launch steps are:

git clone https://github.com/atmos-cloud-sim-uj/PySDM-examples.git
cd PySDM-examples
pip install -e .
jupyter-notebook

PySDM examples (Jupyter notebooks reproducing results from literature):

0D box-model coalescence-only examples (work with both CPU and GPU backends):

Shima et al. 2009 Fig. 2
(Box model, coalescence only, test case employing Golovin analytical solution)
Berry 1967 Figs. 5, 8 & 10
(Box model, coalescence only, test cases for realistic kernels)

0D parcel-model condensation only examples (CPU backend only, stay tuned...)

Arabas & Shima 2017 Fig. 5
(Adiabatic parcel, monodisperse size spectrum activation/deactivation test case)
Yang et al. 2018 Fig. 2:
(Adiabatic parcel, polydisperse size spectrum activation/deactivation test case)

0D parcel-model condensation/aqueous-chemistry example (CPU backend only, stay tuned...)

Kreidenweis et al. 2003 Fig 1:
(Adiabatic parcel, polydisperse size spectrum, aqueous‐phase SO2 oxidation test case)
Jaruga and Pawlowska 2018:
(same test case as above, different numerical settings)

1D kinematic (prescribed-flow, single-column)

Shipway & Hill 2012
(Fig. 1 with thermodynamics & condensation only - no particle displacement)

2D kinematic (prescribed-flow) Sc-mimicking aerosol collisional processing (warm-rain) examples (CPU backend only, stay tuned...)

Arabas et al. 2015 Figs. 8 & 9:
(interactive web-GUI with product selection, parameter sliders and netCDF/plot export buttons)
Bartman et al. 2021 (in preparation):
(default-settings based script generating a netCDF file and loading it subsequently to create the animation below)

Hello-world coalescence example in Python, Julia and Matlab

In order to depict the PySDM API with a practical example, the following listings provide sample code roughly reproducing the Figure 2 from Shima et al. 2009 paper using PySDM from Python, Julia and Matlab. It is a coalescence-only set-up in which the initial particle size spectrum is exponential and is deterministically sampled to match the condition of each super-droplet having equal initial multiplicity:

Julia (click to expand)

using Pkg
Pkg.add("PyCall")
Pkg.add("Plots")

using PyCall
si = pyimport("PySDM.physics").si
ConstantMultiplicity = pyimport("PySDM.initialisation.spectral_sampling").ConstantMultiplicity
Exponential = pyimport("PySDM.initialisation.spectra").Exponential

n_sd = 2^15
initial_spectrum = Exponential(norm_factor=8.39e12, scale=1.19e5 * si.um^3)
attributes = Dict()
attributes["volume"], attributes["n"] = ConstantMultiplicity(spectrum=initial_spectrum).sample(n_sd)

Matlab (click to expand)

si = py.importlib.import_module('PySDM.physics').si;
ConstantMultiplicity = py.importlib.import_module('PySDM.initialisation.spectral_sampling').ConstantMultiplicity;
Exponential = py.importlib.import_module('PySDM.initialisation.spectra').Exponential;

n_sd = 2^15;
initial_spectrum = Exponential(pyargs(...
    'norm_factor', 8.39e12, ...
    'scale', 1.19e5 * si.um ^ 3 ...
));
tmp = ConstantMultiplicity(initial_spectrum).sample(int32(n_sd));
attributes = py.dict(pyargs('volume', tmp{1}, 'n', tmp{2}));

Python

from PySDM.physics import si
from PySDM.initialisation.spectral_sampling import ConstantMultiplicity
from PySDM.initialisation.spectra import Exponential

n_sd = 2**15
initial_spectrum = Exponential(norm_factor=8.39e12, scale=1.19e5 * si.um**3)
attributes = {}
attributes['volume'], attributes['n'] = ConstantMultiplicity(initial_spectrum).sample(n_sd)

The key element of the PySDM interface is the Core class which instances are used to manage the system state and control the simulation. Instantiation of the Core class is handled by the Builder as exemplified below:

Julia (click to expand)

Builder = pyimport("PySDM").Builder
Box = pyimport("PySDM.environments").Box
Coalescence = pyimport("PySDM.dynamics").Coalescence
Golovin = pyimport("PySDM.physics.coalescence_kernels").Golovin
CPU = pyimport("PySDM.backends").CPU
ParticlesVolumeSpectrum = pyimport("PySDM.products.state").ParticlesVolumeSpectrum

builder = Builder(n_sd=n_sd, backend=CPU)
builder.set_environment(Box(dt=1 * si.s, dv=1e6 * si.m^3))
builder.add_dynamic(Coalescence(kernel=Golovin(b=1.5e3 / si.s)))
products = [ParticlesVolumeSpectrum()] 
particles = builder.build(attributes, products)

Matlab (click to expand)

Builder = py.importlib.import_module('PySDM').Builder;
Box = py.importlib.import_module('PySDM.environments').Box;
Coalescence = py.importlib.import_module('PySDM.dynamics').Coalescence;
Golovin = py.importlib.import_module('PySDM.physics.coalescence_kernels').Golovin;
CPU = py.importlib.import_module('PySDM.backends').CPU;
ParticlesVolumeSpectrum = py.importlib.import_module('PySDM.products.state').ParticlesVolumeSpectrum;

builder = Builder(pyargs('n_sd', int32(n_sd), 'backend', CPU));
builder.set_environment(Box(pyargs('dt', 1 * si.s, 'dv', 1e6 * si.m ^ 3)));
builder.add_dynamic(Coalescence(pyargs('kernel', Golovin(1.5e3 / si.s))));
products = py.list({ ParticlesVolumeSpectrum() });
particles = builder.build(attributes, products);

Python

from PySDM import Builder
from PySDM.environments import Box
from PySDM.dynamics import Coalescence
from PySDM.physics.coalescence_kernels import Golovin
from PySDM.backends import CPU
from PySDM.products.state import ParticlesVolumeSpectrum

builder = Builder(n_sd=n_sd, backend=CPU)
builder.set_environment(Box(dt=1 * si.s, dv=1e6 * si.m**3))
builder.add_dynamic(Coalescence(kernel=Golovin(b=1.5e3 / si.s)))
products = [ParticlesVolumeSpectrum()]
particles = builder.build(attributes, products)

The backend argument may be set to CPU or GPU what translates to choosing the multi-threaded backend or the GPU-resident computation mode, respectively. The employed Box environment corresponds to a zero-dimensional framework (particle positions are not considered). The vectors of particle multiplicities n and particle volumes v are used to initialise super-droplet attributes. The Coalescence Monte-Carlo algorithm (Super Droplet Method) is registered as the only dynamic in the system (other available dynamics representing condensational growth and particle displacement). Finally, the build() method is used to obtain an instance of Core which can then be used to control time-stepping and access simulation state.

The run(nt) method advances the simulation by nt timesteps. In the listing below, its usage is interleaved with plotting logic which displays a histogram of particle mass distribution at selected timesteps:

Julia (click to expand)

rho_w = pyimport("PySDM.physics.constants").rho_w
using Plots

radius_bins_edges = 10 .^ range(log10(10*si.um), log10(5e3*si.um), length=32) 

for step = 0:1200:3600
    particles.run(step - particles.n_steps)
    plot!(
        radius_bins_edges[1:end-1] / si.um,
        particles.products["dv/dlnr"].get(radius_bins_edges) * rho_w / si.g,
        linetype=:steppost,
        xaxis=:log,
        xlabel="particle radius [µm]",
        ylabel="dm/dlnr [g/m^3/(unit dr/r)]",
        label="t = $step s"
    )   
end
savefig("plot.svg")

Matlab (click to expand)

rho_w = py.importlib.import_module('PySDM.physics.constants').rho_w;

radius_bins_edges = logspace(log10(10 * si.um), log10(5e3 * si.um), 32);

for step = 0:1200:3600
    particles.run(int32(step - particles.n_steps))
    x = radius_bins_edges / si.um;
    y = particles.products{"dv/dlnr"}.get(py.numpy.array(radius_bins_edges)) * rho_w / si.g;
    stairs(...
        x(1:end-1), ... 
        double(py.array.array('d',py.numpy.nditer(y))), ...
        'DisplayName', sprintf("t = %d s", step) ...
    );
    hold on
end
hold off
set(gca,'XScale','log');
xlabel('particle radius [µm]')
ylabel("dm/dlnr [g/m^3/(unit dr/r)]")
legend()

Python

from PySDM.physics.constants import rho_w
from matplotlib import pyplot
import numpy as np

radius_bins_edges = np.logspace(np.log10(10 * si.um), np.log10(5e3 * si.um), num=32)

for step in [0, 1200, 2400, 3600]:
    particles.run(step - particles.n_steps)
    pyplot.step(x=radius_bins_edges[:-1] / si.um,
                y=particles.products['dv/dlnr'].get(radius_bins_edges) * rho_w / si.g,
                where='post', label=f"t = {step}s")

pyplot.xscale('log')
pyplot.xlabel('particle radius [µm]')
pyplot.ylabel("dm/dlnr [g/m$^3$/(unit dr/r)]")
pyplot.legend()
pyplot.savefig('readme.svg')

The resultant plot looks as follows:

Hello-world condensation example in Python, Julia and Matlab

Julia (click to expand)

using PyCall
using Plots
si = pyimport("PySDM.physics").si
spectral_sampling = pyimport("PySDM.initialisation").spectral_sampling
multiplicities = pyimport("PySDM.initialisation").multiplicities
spectra = pyimport("PySDM.initialisation").spectra
r_wet_init = pyimport("PySDM.initialisation").r_wet_init
CPU = pyimport("PySDM.backends").CPU
AmbientThermodynamics = pyimport("PySDM.dynamics").AmbientThermodynamics
Condensation = pyimport("PySDM.dynamics").Condensation
Parcel = pyimport("PySDM.environments").Parcel
Builder = pyimport("PySDM").Builder
products = pyimport("PySDM.products")

env = Parcel(
    dt=.25 * si.s,
    mass_of_dry_air=1e3 * si.kg,
    p0=1122 * si.hPa,
    q0=20 * si.g / si.kg,
    T0=300 * si.K,
    w= 2.5 * si.m / si.s
)
spectrum=spectra.Lognormal(norm_factor=1e4/si.mg, m_mode=50*si.nm, s_geom=1.4)
kappa = .5 * si.dimensionless
cloud_range = (.5 * si.um, 25 * si.um)
output_interval = 4
output_points = 40
n_sd = 256

builder = Builder(backend=CPU, n_sd=n_sd)
builder.set_environment(env)
builder.add_dynamic(AmbientThermodynamics())
builder.add_dynamic(Condensation(kappa=kappa))

r_dry, specific_concentration = spectral_sampling.Logarithmic(spectrum).sample(n_sd)
r_wet = r_wet_init(r_dry, env, kappa)

attributes = Dict()
attributes["n"] = multiplicities.discretise_n(specific_concentration * env.mass_of_dry_air)
attributes["dry volume"] = builder.formulae.trivia.volume(radius=r_dry)
attributes["volume"] = builder.formulae.trivia.volume(radius=r_wet) 

particles = builder.build(attributes, products=[
    products.PeakSupersaturation(),
    products.CloudDropletEffectiveRadius(radius_range=cloud_range),
    products.CloudDropletConcentration(radius_range=cloud_range),
    products.WaterMixingRatio(radius_range=cloud_range)
])
    
cell_id=1
output = Dict("z" => Array{Float32}(undef, output_points+1))
for (_, product) in particles.products
    output[product.name] = Array{Float32}(undef, output_points+1)
    output[product.name][1] = product.get()[cell_id]
end 
output["z"][1] = env.__getitem__("z")[cell_id]
    
for step = 2:output_points+1
    particles.run(steps=output_interval)
    for (_, product) in particles.products
        output[product.name][step] = product.get()[cell_id]
    end 
    output["z"][step]=env.__getitem__("z")[cell_id]
end 

plots = []
for (_, product) in particles.products
    append!(plots, [plot(output[product.name], output["z"], ylabel="z [m]", xlabel=product.unit, title=product.name)])
end
plot(plots..., layout=(1,4))
savefig("parcel.svg")

Matlab (click to expand)

si = py.importlib.import_module('PySDM.physics').si;
spectral_sampling = py.importlib.import_module('PySDM.initialisation').spectral_sampling;
multiplicities = py.importlib.import_module('PySDM.initialisation').multiplicities;
spectra = py.importlib.import_module('PySDM.initialisation').spectra;
r_wet_init = py.importlib.import_module('PySDM.initialisation').r_wet_init;
CPU = py.importlib.import_module('PySDM.backends').CPU;
AmbientThermodynamics = py.importlib.import_module('PySDM.dynamics').AmbientThermodynamics;
Condensation = py.importlib.import_module('PySDM.dynamics').Condensation;
Parcel = py.importlib.import_module('PySDM.environments').Parcel;
Builder = py.importlib.import_module('PySDM').Builder;
products = py.importlib.import_module('PySDM.products');

env = Parcel(pyargs( ...
    'dt', .25 * si.s, ...
    'mass_of_dry_air', 1e3 * si.kg, ...
    'p0', 1122 * si.hPa, ...
    'q0', 20 * si.g / si.kg, ...
    'T0', 300 * si.K, ...
    'w', 2.5 * si.m / si.s ...
));
spectrum = spectra.Lognormal(pyargs('norm_factor', 1e4/si.mg, 'm_mode', 50 * si.nm, 's_geom', 1.4));
kappa = .5;
cloud_range = py.tuple({.5 * si.um, 25 * si.um});
output_interval = 1;
output_points = 40;
n_sd = 256;

builder = Builder(pyargs('backend', CPU, 'n_sd', int32(n_sd)));
builder.set_environment(env);
builder.add_dynamic(AmbientThermodynamics())
builder.add_dynamic(Condensation(pyargs('kappa', kappa)))

tmp = spectral_sampling.Logarithmic(spectrum).sample(int32(n_sd));
r_dry = tmp{1};
specific_concentration = tmp{2};
r_wet = r_wet_init(r_dry, env, kappa);

attributes = py.dict(pyargs( ...
    'n', multiplicities.discretise_n(specific_concentration * env.mass_of_dry_air), ...
    'dry volume', builder.formulae.trivia.volume(r_dry), ...
    'volume', builder.formulae.trivia.volume(r_wet) ...
));

particles = builder.build(attributes, py.list({ ...
    products.PeakSupersaturation(), ...
    products.CloudDropletEffectiveRadius(pyargs('radius_range', cloud_range)), ...
    products.CloudDropletConcentration(pyargs('radius_range', cloud_range)), ...
    products.WaterMixingRatio(pyargs('radius_range', cloud_range)) ...
}));

cell_id = int32(0);
output_size = [output_points+1, 1 + length(py.list(particles.products.keys()))];
output_types = repelem({'double'}, output_size(2));
output_names = ['z', cellfun(@string, cell(py.list(particles.products.keys())))];
output = table(...
    'Size', output_size, ...
    'VariableTypes', output_types, ...
    'VariableNames', output_names ...
);
for pykey = py.list(keys(particles.products))
    get = py.getattr(particles.products{pykey{1}}.get(), '__getitem__');
    key = string(pykey{1});
    output{1, key} = get(cell_id);
end
get = py.getattr(env, '__getitem__');
zget = py.getattr(get('z'), '__getitem__');
output{1, 'z'} = zget(cell_id);

for i=2:output_points+1
    particles.run(pyargs('steps', int32(output_interval)));
    for pykey = py.list(keys(particles.products))
        get = py.getattr(particles.products{pykey{1}}.get(), '__getitem__');
        key = string(pykey{1});
        output{i, key} = get(cell_id);
    end
    output{i, 'z'} = zget(cell_id);
end

i=1;
for pykey = py.list(keys(particles.products))
    product = particles.products{pykey{1}};
    subplot(1, width(output)-1, i);
    plot(output{:, string(pykey{1})}, output.z);
    title(string(product.name));
    xlabel(string(product.unit));
    ylabel('z [m]');
    i=i+1;
end

Python

from matplotlib import pyplot
from PySDM.physics import si
from PySDM.initialisation import spectral_sampling, multiplicities, spectra, r_wet_init
from PySDM.backends import CPU
from PySDM.dynamics import AmbientThermodynamics, Condensation
from PySDM.environments import Parcel
from PySDM import Builder, products

env = Parcel(
    dt=.25 * si.s,
    mass_of_dry_air=1e3 * si.kg,
    p0=1122 * si.hPa,
    q0=20 * si.g / si.kg,
    T0=300 * si.K,
    w=2.5 * si.m / si.s
)
spectrum = spectra.Lognormal(norm_factor=1e4/si.mg, m_mode=50*si.nm, s_geom=1.5)
kappa = .5 * si.dimensionless
cloud_range = (.5 * si.um, 25 * si.um)
output_interval = 4
output_points = 40
n_sd = 256

builder = Builder(backend=CPU, n_sd=n_sd)
builder.set_environment(env)
builder.add_dynamic(AmbientThermodynamics())
builder.add_dynamic(Condensation(kappa=kappa))

r_dry, specific_concentration = spectral_sampling.Logarithmic(spectrum).sample(n_sd)
r_wet = r_wet_init(r_dry, env, kappa)

attributes = {
    'n': multiplicities.discretise_n(specific_concentration * env.mass_of_dry_air),
    'dry volume': builder.formulae.trivia.volume(radius=r_dry),
    'volume': builder.formulae.trivia.volume(radius=r_wet)
}

particles = builder.build(attributes, products=[
    products.PeakSupersaturation(),
    products.CloudDropletEffectiveRadius(radius_range=cloud_range),
    products.CloudDropletConcentration(radius_range=cloud_range),
    products.WaterMixingRatio(radius_range=cloud_range)
])

cell_id = 0
output = {product.name: [product.get()[cell_id]] for product in particles.products.values()}
output['z'] = [env['z'][cell_id]]

for step in range(output_points):
    particles.run(steps=output_interval)
    for product in particles.products.values():
        output[product.name].append(product.get()[cell_id])
    output['z'].append(env['z'][cell_id])

fig, axs = pyplot.subplots(1, len(particles.products), sharey="all")
for i, (key, product) in enumerate(particles.products.items()):
    axs[i].plot(output[key], output['z'], marker='.')
    axs[i].set_title(product.name)
    axs[i].set_xlabel(product.unit)
    axs[i].grid()
pyplot.savefig('parcel.svg')

Package structure and API

backends:
- CPU=Numba: multi-threaded CPU backend using LLVM-powered just-in-time compilation
- GPU=ThrustRTC: GPU-resident backend using NVRTC runtime compilation library for CUDA
initialisation:
- multiplicities: integer-valued discretisation with sanity checks for errors due to type casting
- r_wet_init: kappa-Keohler-based equilibrium in unsaturated conditions (RH=1 used in root-finding above saturation)
- spatial_sampling: pseudorandom sampling using NumPy's default RNG
- spectra: Exponential and Lognormal classes
- spectral_sampling: linear, logarithmic and constant_multiplicity classes
physics:
- coalescence_kernels (selected)
  - Golovin
  - Geometric
  - Hydrodynamic
  - ...
- constants: physical constants partly imported from SciPy and chempy packages
- dimensional_analysis: tool for enabling dimensional analysis of the code for unit tests (based on pint)
- formulae: physical formulae boosted with Numba (e.g., for initialisation)
environments:
- Box: bare zero-dimensional framework
- Parcel: zero-dimensional adiabatic parcel framework
- Kinematic1D: single-column time-varying-updraft framework with moisture advection handled by PyMPDATA
- Kinematic2D: two-dimensional single-eddy prescribed-flow framework with moisture and heat advection handled by PyMPDATA
dynamics:
- Coalescence: SDM implementation with adaptive timestepping
- Condensation: bespoke solver with implicit-in-particle-size integration and adaptive timestepping (Numba only as of now, soon on all backends)
- AqueousChemistry: aqueous-phase chemistry (incl. SO2 oxidation)
- Displacement: includes advection with the flow & sedimentation
- EulerianAdvection: wrapper class for triggering integration in the Eulerian advection solver underlying used by the selected environment
Attributes (selected):
- numerics:
  - position_in_cell
  - cell_id
  - ...
- physics:
  - volume
  - multiplicities
  - critical_volume
  - ...
- chemistry:
  - pH
  - concentration
  - ...
Products (selected):

Credits:

Development of PySDM is supported by the EU through a grant of the Foundation for Polish Science (POIR.04.04.00-00-5E1C/18).

copyright: Jagiellonian University
licence: GPL v3

Related resources and open-source projects

SDM patents (some expired, some withdrawn):

https://patents.google.com/patent/US7756693B2
https://patents.google.com/patent/EP1847939A3
https://patents.google.com/patent/JP4742387B2
https://patents.google.com/patent/CN101059821B

Other SDM implementations:

SCALE-SDM (Fortran):
https://github.com/Shima-Lab/SCALE-SDM_BOMEX_Sato2018/blob/master/contrib/SDM/sdm_coalescence.f90
Pencil Code (Fortran):
https://github.com/pencil-code/pencil-code/blob/master/src/particles_coagulation.f90
PALM LES (Fortran):
https://palm.muk.uni-hannover.de/trac/browser/palm/trunk/SOURCE/lagrangian_particle_model_mod.f90
libcloudph++ (C++):
https://github.com/igfuw/libcloudphxx/blob/master/src/impl/particles_impl_coal.ipp
LCM1D (Python)
https://github.com/SimonUnterstrasser/ColumnModel
superdroplet (Cython/Numba/C++11/Fortran 2008/Julia)
https://github.com/darothen/superdroplet
NTLP (FORTRAN)
https://github.com/Folca/NTLP/blob/SuperDroplet/les.F

non-SDM probabilistic particle-based coagulation solvers

PartMC (Fortran):
https://github.com/compdyn/partmc

Python models with discrete-particle (moving-sectional) representation of particle size spectrum

pyrcel: https://github.com/darothen/pyrcel
PyBox: https://github.com/loftytopping/PyBox
py-cloud-parcel-model: https://github.com/emmasimp/py-cloud-parcel-model

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README.md

README.md

PySDM

Dependencies and Installation

PySDM examples (Jupyter notebooks reproducing results from literature):

0D box-model coalescence-only examples (work with both CPU and GPU backends):

0D parcel-model condensation only examples (CPU backend only, stay tuned...)

0D parcel-model condensation/aqueous-chemistry example (CPU backend only, stay tuned...)

1D kinematic (prescribed-flow, single-column)

2D kinematic (prescribed-flow) Sc-mimicking aerosol collisional processing (warm-rain) examples (CPU backend only, stay tuned...)

Hello-world coalescence example in Python, Julia and Matlab

Hello-world condensation example in Python, Julia and Matlab

Package structure and API

Credits:

Related resources and open-source projects

SDM patents (some expired, some withdrawn):

Other SDM implementations:

non-SDM probabilistic particle-based coagulation solvers

Python models with discrete-particle (moving-sectional) representation of particle size spectrum

Files

README.md

Latest commit

History

README.md

File metadata and controls

PySDM

Dependencies and Installation

PySDM examples (Jupyter notebooks reproducing results from literature):

0D box-model coalescence-only examples (work with both CPU and GPU backends):

0D parcel-model condensation only examples (CPU backend only, stay tuned...)

0D parcel-model condensation/aqueous-chemistry example (CPU backend only, stay tuned...)

1D kinematic (prescribed-flow, single-column)

2D kinematic (prescribed-flow) Sc-mimicking aerosol collisional processing (warm-rain) examples (CPU backend only, stay tuned...)

Hello-world coalescence example in Python, Julia and Matlab

Hello-world condensation example in Python, Julia and Matlab

Package structure and API

Credits:

Related resources and open-source projects

SDM patents (some expired, some withdrawn):

Other SDM implementations:

non-SDM probabilistic particle-based coagulation solvers

Python models with discrete-particle (moving-sectional) representation of particle size spectrum