settling Process Documentation¶

Overview¶

Gravitational settling process for atmospheric particles implementing physics-based settling schemes with temperature-dependent viscosity, slip correction, and robust numerical integration.

Process Type: transport Author: CATChem Development Team Version: 1.0 Date: 2025

Features¶

Available Schemes¶

Stokesscheme: Advanced Stokes settling with Cunningham slip correction and temperature-dependent dynamic viscosity
Sutherland's formula for dynamic viscosity
Cunningham slip correction for small particles
CFL-stable time integration with automatic subcycling
Support for non-spherical particles via shape factors
Robust error handling and bounds checking
Intermediatereynoldsscheme: Intermediate Reynolds number settling scheme for larger particles

Physical Features¶

Dynamic viscosity: Temperature-dependent air viscosity using Sutherland's law
Slip correction: Cunningham slip correction for particles smaller than mean free path
Shape factors: Support for non-spherical particles
CFL stability: Automatic subcycling to maintain numerical stability
Error handling: Comprehensive bounds checking and validation

Usage¶

Initialization¶

use settlingProcess_Mod
type(settlingProcessType) :: process
type(StateContainerType) :: container
integer :: rc

! Initialize the process
call process%init(container, rc)

Running the Process¶

! Run the process
call process%run(container, rc)

Finalization¶

! Clean up
call process%finalize(rc)

Configuration¶

The settling process requires particle properties and meteorological data to calculate settling velocities.

Required Meteorological Fields¶

temperature: Air temperature [K]
pressure: Air pressure [Pa]
air_density: Air density [kg/m³]

Required Tracer Properties¶

particle_radius: Effective particle radius [m]
particle_density: Particle density [kg/m³]

Optional Tracer Properties¶

shape_factor: Dynamic shape factor for non-spherical particles [dimensionless, default: 1.0]

Available Diagnostics¶

settling_velocity: Gravitational settling velocity [m/s]
settling_flux: Vertical settling mass flux [kg/m²/s]
cfl_number: CFL number for settling time step [dimensionless]
dynamic_viscosity: Temperature-dependent air dynamic viscosity [kg/m/s]
slip_correction: Cunningham slip correction factor [dimensionless]

Physical Equations¶

Stokes Settling Velocity¶

The basic Stokes settling velocity is calculated as:

v_s = (2 * g * (ρ_p - ρ_air) * r²) / (9 * μ)

Where: - g = gravitational acceleration [9.81 m/s²] - ρ_p = particle density [kg/m³] - ρ_air = air density [kg/m³] - r = particle radius [m] - μ = dynamic viscosity [kg/m/s]

Dynamic Viscosity (Sutherland's Law)¶

μ(T) = μ₀ * T^1.5 / (T + S)

Where: - μ₀ = 1.458e-6 kg/(m·s·K^1.5) - S = 110.4 K (Sutherland temperature) - T = temperature [K]

Cunningham Slip Correction¶

C_c = 1 + (λ/r) * [A₁ + A₂ * exp(-A₃ * r/λ)]

Where: - λ = mean free path [m] - A₁ = 1.257, A₂ = 0.4, A₃ = 1.1 (slip coefficients)

Final Settling Velocity¶

v_settling = v_s * C_c / χ

Where χ is the dynamic shape factor for non-spherical particles.

Implementation Details¶

Process Structure¶

src/process/settling/
├── settlingProcess_Mod.F90     # Main process module
├── settlingCommon_Mod.F90      # Common utilities
└── schemes/                               # Scheme implementations
    ├── StokesschemeScheme_Mod.F90
    ├── IntermediatereynoldsschemeScheme_Mod.F90

Testing¶

Unit tests are available in:

tests/process/settling/
└── test_settling_process.F90

Run tests with:

ctest -R settling