project_n: Project values for first time step of Euler method

In mizer: Dynamic Multi-Species Size Spectrum Modelling

Project values for first time step of Euler method

Description

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. See project().

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.

Value

The updated abundance density matrix n.

See Also

project, mizerRates

mizer documentation built on Aug. 31, 2026, 5:08 p.m.