Functions/Subroutines

pmc_coag_kernel_constant Module Reference

Constant coagulation kernel. More...

Functions/Subroutines

subroutine kernel_constant (aero_particle_1, aero_particle_2, aero_data, env_state, k)
 Constant coagulation kernel.
subroutine kernel_constant_max (v1, v2, aero_data, env_state, k_max)
 Maximum value of the constant coagulation kernel.
subroutine soln_constant_exp (bin_grid, aero_data, time, num_conc, radius_at_mean_vol, env_state, aero_binned)
 Exact solution with a constant coagulation kernel and an exponential initial condition.

Detailed Description

Constant coagulation kernel.


Function/Subroutine Documentation

subroutine pmc_coag_kernel_constant::kernel_constant ( type(aero_particle_t),intent(in)  aero_particle_1,
type(aero_particle_t),intent(in)  aero_particle_2,
type(aero_data_t),intent(in)  aero_data,
type(env_state_t),intent(in)  env_state,
real(kind=dp),intent(out)  k 
)

Constant coagulation kernel.

Parameters:
aero_particle_1First particle.
aero_particle_2Second particle.
aero_dataAerosol data.
env_stateEnvironment state.
kCoagulation kernel.
subroutine pmc_coag_kernel_constant::kernel_constant_max ( real(kind=dp),intent(in)  v1,
real(kind=dp),intent(in)  v2,
type(aero_data_t),intent(in)  aero_data,
type(env_state_t),intent(in)  env_state,
real(kind=dp),intent(out)  k_max 
)

Maximum value of the constant coagulation kernel.

Parameters:
v1Volume of first particle.
v2Volume of second particle.
aero_dataAerosol data.
env_stateEnvironment state.
k_maxCoagulation kernel maximum value.
subroutine pmc_coag_kernel_constant::soln_constant_exp ( type(bin_grid_t),intent(in)  bin_grid,
type(aero_data_t),intent(in)  aero_data,
real(kind=dp),intent(in)  time,
real(kind=dp),intent(in)  num_conc,
real(kind=dp),intent(in)  radius_at_mean_vol,
type(env_state_t),intent(in)  env_state,
type(aero_binned_t),intent(inout)  aero_binned 
)

Exact solution with a constant coagulation kernel and an exponential initial condition.

Given input paramaters $R$ and $N_0$ we let the mean volume be $v_\mu = \frac{4\pi}{3} R^3$ and define the rescaled time $\tau = N_0 \beta_0 t$, where $\beta_0$ is the fixed constant kernel value. We also set the parameter $\lambda = 1$. Then the solution is

\[ n(D,t) \ {\rm d}\ln D = \frac{\pi}{2} D^3 \frac{N_0}{v_\mu} \frac{4}{(\tau + 2)^2} \exp\left(-\frac{v}{v_\mu} \frac{2}{\tau + 2} \exp(-\lambda \tau) - \lambda \tau\right) {\rm d}\ln D \]

This thus has initial condition

\[ n(D,t) \ {\rm d}\ln D = \frac{\pi}{2} D^3 \frac{N_0}{v_\mu} \exp\left(-\frac{v}{v_\mu}\right) {\rm d}\ln D \]

Parameters:
bin_gridBin grid.
aero_dataAerosol data.
timeCurrent time.
num_concParticle number concentration (#/m^3).
radius_at_mean_volMean init radius (m).
env_stateEnvironment state.
aero_binnedOutput state.