pmc_kernel_zero Namespace Reference

Constant kernel equal to zero. More...


Functions

subroutine kernel_zero (v1, v2, env_state, k)
 Zero coagulation kernel.
subroutine soln_zero (bin_grid, aero_data, time, num_den, mean_vol, rho_p, aero_dist_init, env_state, aero_binned)
 Exact solution with the zero coagulation kernel. Only useful for testing emissions and background dilution.


Detailed Description

Constant kernel equal to zero.

This is only of interest for the exact solution to the no-coagulation, no-condensation case that can be used to test emissions and background dilution.


Function Documentation

subroutine pmc_kernel_zero::kernel_zero ( real*8,intent(in)  v1,
real*8,intent(in)  v2,
type(env_state_t),intent(in)  env_state,
real*8,intent(out)  k 
)

Zero coagulation kernel.

Parameters:
v1  Volume of first particle.
v2  Volume of second particle.
env_state  Environment state.
k  Coagulation kernel.

subroutine pmc_kernel_zero::soln_zero ( type(bin_grid_t),intent(in)  bin_grid,
type(aero_data_t),intent(in)  aero_data,
real*8,intent(in)  time,
real*8,intent(in)  num_den,
real*8,intent(in)  mean_vol,
real*8,intent(in)  rho_p,
type(aero_dist_t),intent(in)  aero_dist_init,
type(env_state_t),intent(in)  env_state,
type(aero_binned_t),intent(out)  aero_binned 
)

Exact solution with the zero coagulation kernel. Only useful for testing emissions and background dilution.

With only emissions and dilution the number distribution $ n(r,t) $ satisfies:

\[ \frac{d n(r,t)}{dt} = k_{\rm emit} n_{\rm emit}(r) + k_{\rm dilute} (n_{\rm back}(r) - n(r,t)) \]

together with the initial condition $ n(r,0) = n_0(r) $. Here $ n_{\rm emit}(r) $ and $ n_{\rm back}(r) $ are emission and background size distributions, with corresponding rates $ k_{\rm emit} $ and $ k_{\rm dilute} $.

This is a family of ODEs parameterized by $ r $ with solution:

\[ n(r,t) = n_{\infty}(r) + (n_0(r) - n_{\infty}(r)) \exp(-k_{\rm dilute} t) \]

where the steady state limit is:

\[ n_{\infty}(r) = n(r,\infty) = n_{\rm back}(r) + \frac{k_{\rm emit}}{k_{\rm dilute}} n_{\rm emit}(r) \]

Parameters:
bin_grid  Bin grid.
aero_data  Aerosol data.
time  Current time (s).
num_den  Particle number concentration (#/m^3).
mean_vol  Mean init volume (m^3).
rho_p  Particle density (kg/m^3).
aero_dist_init  Initial distribution.
env_state  Environment state.
aero_binned  Output state.


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