Additive coagulation kernel. More...

Functions/Subroutines
subroutine	kernel_additive (aero_particle_1, aero_particle_2, aero_data, env_state, k)
	Additive coagulation kernel. More...

subroutine	kernel_additive_minmax (v1, v2, aero_data, env_state, k_min, k_max)
	Minimum and maximum values of the additive kernel. More...

subroutine	soln_additive_exp (bin_grid, aero_data, time, num_conc, radius_at_mean_vol, env_state, aero_binned)
	Exact solution with the additive coagulation kernel and exponential initial condition. More...

subroutine	bessi1 (x, r)
	Modified Bessel function of the first kind . More...

subroutine	calci1 (arg, result, jint)
	Calculates modified Bessel functions of the first kind . More...

Variables
real(kind=dp), parameter	beta_1 = 1000d0
	Scaling coefficient for constant kernel. More...

Detailed Description

Additive coagulation kernel.

Function/Subroutine Documentation

◆ bessi1()

subroutine pmc_coag_kernel_additive::bessi1	(	real(kind=dp), intent(in)	x,
		real(kind=dp), intent(out)	r
	)

Modified Bessel function of the first kind .

Parameters

[in]	x	Function argument.
[out]	r	Function value.

Definition at line 172 of file coag_kernel_additive.F90.

◆ calci1()

subroutine pmc_coag_kernel_additive::calci1	(	real ( kind = 8 )	arg,
		real ( kind = 8 )	result,
		integer ( kind = 4 )	jint
	)

Calculates modified Bessel functions of the first kind .

Definition at line 186 of file coag_kernel_additive.F90.

◆ kernel_additive()

subroutine pmc_coag_kernel_additive::kernel_additive	(	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
	)

Additive coagulation kernel.

Parameters

[in]	aero_particle_1	First particle.
[in]	aero_particle_2	Second particle.
[in]	aero_data	Aerosol data.
[in]	env_state	Environment state.
[out]	k	Coagulation kernel.

Definition at line 30 of file coag_kernel_additive.F90.

◆ kernel_additive_minmax()

subroutine pmc_coag_kernel_additive::kernel_additive_minmax	(	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_min,
		real(kind=dp), intent(out)	k_max
	)

Minimum and maximum values of the additive kernel.

Parameters

[in]	v1	Volume of first particle.
[in]	v2	Volume of second particle.
[in]	aero_data	Aerosol data.
[in]	env_state	Environment state.
[out]	k_min	Coagulation kernel minimum value.
[out]	k_max	Coagulation kernel maximum value.

Definition at line 52 of file coag_kernel_additive.F90.

◆ soln_additive_exp()

subroutine pmc_coag_kernel_additive::soln_additive_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 the additive coagulation kernel and exponential initial condition.

Given input paramaters and we let the mean volume be $v_\mu = \frac{4\pi}{3} R^3$ and define the rescaled times $\tau = N_0 v_\mu \beta_1 t$ and $T = 1 - e^{-\tau}$ , where $\beta_1$ is the fixed kernel scaling parameter. Then the solution is

$n(D,t) \ {\rm d}\ln D = \frac{\pi}{2} D^3 \frac{N_0}{v} \frac{1 - T}{\sqrt{T}} \exp\left(-(1 + T) \frac{v}{v_\mu}\right) I_1\left(2 \frac{v}{v_\mu} \sqrt{T}\right) {\rm d}\ln D$

where is the modified Bessel function of the first kind and $v = \frac{\pi}{6} D^3$ .

For small we have $I_1(x) \approx \frac{x}{2}$ , so this solution 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

[in]	bin_grid	Bin grid.
[in]	aero_data	Aerosol data.
[in]	time	Current time.
[in]	num_conc	Particle number concentration (#/m^3).
[in]	radius_at_mean_vol	Mean init radius (m).
[in]	env_state	Environment state.
[in,out]	aero_binned	Output state.

Definition at line 101 of file coag_kernel_additive.F90.

Variable Documentation

◆ beta_1

real(kind=dp), parameter pmc_coag_kernel_additive::beta_1 = 1000d0

Scaling coefficient for constant kernel.

Definition at line 23 of file coag_kernel_additive.F90.

Functions/Subroutines

Variables

Detailed Description

Function/Subroutine Documentation

◆ bessi1()

◆ calci1()

◆ kernel_additive()

◆ kernel_additive_minmax()

◆ soln_additive_exp()

Variable Documentation

◆ beta_1