This is an internal function used by the user-facing project() function.
It is of potential interest only to mizer extension authors.
Usage
project_n(
params,
r,
n,
dt,
a,
b,
c,
S,
idx,
w_min_idx_array_ref,
no_sp,
no_w,
flux_limiter = "none"
)
project_n_no_diffusion(
params,
r,
n,
dt,
a,
b,
S,
idx,
w_min_idx_array_ref,
no_sp,
no_w
)Arguments
- params
A MizerParams object.
- r
A list of rates as returned by
mizerRates().- n
An array (species x size) with the number density at the current time step.
- dt
Time step.
- a
A matrix (species x size) used in the solver (transport term).
- b
A matrix (species x size) used in the solver (diagonal term).
- c
A matrix (species x size) used in the solver (transport term).
- S
A matrix (species x size) used in the solver (source term).
- idx
Index vector for size bins (excluding the first one).
- w_min_idx_array_ref
Index vector for the start of the size spectrum for each species.
- no_sp
Number of species.
- no_w
Number of size bins.
- flux_limiter
Name of the flux limiter used for a deferred high-order correction of the upwind advective flux, or
"none"for plain first-order upwind. Seeproject().
Details
The function calculates the abundance at the next time step using the McKendrick-von Foerster equation: $$\frac{\partial N}{\partial t} + \frac{\partial}{\partial w} \left( g N - \frac{1}{2}\frac{\partial(D N)}{\partial w} \right) = -\mu N$$ which is solved using a semi-implicit upwind finite volume scheme.