Particle propagator

PushVinViscousPotential

Advances fluid.

What it solves

For each marker

p

, solves

\frac{d v _{p} ( t )}{d t} = κ_{p} i = 1 \sum N w_{i} (\frac{1}{ρ ^{N, h} ( η _{p} )} + \frac{1}{ρ ^{N, h} ( η _{i} )}) D F^{- ⊤} \nabla W_{h} (η_{p} - η_{i}),

where $D F^{- ⊤}$ denotes the inverse transpose Jacobian, and with the smoothed density

ρ^{N, h} (η) = \frac{1}{N} j = 1 \sum N w_{j} W_{h} (η - η_{j}),

where $W_{h} (η)$ is a smoothing kernel from struphy.pic.sph_smoothing_kernels. Time stepping:

* 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
`fluid`	SPHVariable	`ParticlesSPH`

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

Option	Default	Choices	Description
`kernel_type`	`gaussian_2d`	`trigonometric_1dgaussian_1dlinear_1dtrigonometric_2dgaussian_2dlinear_2dtrigonometric_3dgaussian_3dlinear_isotropic_3dlinear_3d`	Smoothing kernel used for SPH evaluations.
`kernel_width`	`None`	tuple	Kernel widths per logical direction. If `None`, defaults to `(1 / n_i)` based on sorting boxes.
`algo`	`forward_euler`	`forward_euler`	Time stepping algorithm for the viscous potential push.
`mu`	`1`	float	Dynamic viscosity coefficient used by the viscosity tensor kernel. Must be non-negative.

Each model splits its time step into a sequence of propagators. This one appears in 2 models, at the position shown.