Particle propagator

PushDeterministicDiffusion

Advances var.

What it solves

For each marker

p

, solves

\frac{d x _{p} ( t )}{d t} = - D \frac{\nabla u}{u} (x_{p} (t)),

in logical space given by $x = F (η)$ :

\frac{d η _{p} ( t )}{d t} = - G D \frac{\nabla Π _{L^{2}}^{0} u _{h}}{Π _{L^{2}}^{0} u _{h}} (η_{p} (t)), [Π_{L^{2}, ij k}^{0} u_{h}] (η_{p}) = \frac{1}{N} p \sum w_{p} Λ_{ij k}^{0} (η_{p}),

where $D > 0$ is a positive diffusion coefficient.

Available algorithms:

* Explicit from struphy.ode.utils.ButcherTableau

The variables this step updates over a time step dt, and the discrete spaces each one accepts.

Name	Kind	Accepted spaces
`var`	PICVariable	`Particles3D`

Set these on the propagator in a parameter file, for example PushDeterministicDiffusion.Options(butcher=...).

Option	Default	Choices	Description
`butcher`	`None`	ButcherTableau	Butcher tableau used for explicit Runge-Kutta integration. If `None`, defaults to `ButcherTableau()`.
`bc_type`	`('periodic', 'periodic', 'periodic')`	tuple	Boundary-condition types per logical coordinate.
`diff_coeff`	`1`	float	Positive deterministic diffusion coefficient $D$ .

Each model splits its time step into a sequence of propagators. This one appears in 1 model, at the position shown.