Particle propagator

PushVinSPHpressure

Advances fluid.

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What it solves

For each marker

p

, solves

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

where $g$ is a constant acceleration and the second term corresponds to the pressure gradient. Here, $U (ρ)$ denotes the internal energy per unit mass as a function of the mass density $ρ$ and $D F^{- ⊤}$ denotes the inverse transpose Jacobian arising in the pull back of the gradient of the smoothing kernel $W_{h}$ chosen from struphy.pic.sph_smoothing_kernels. Two choices of the internal energy are implemented:

Isothermal closure: $U (ρ) = κ ln (ρ)$ , where $κ$ is constant. Polytropic closure: $U (ρ) = κ ρ^{γ - 1} / (γ - 1)$ , where $κ$ is the polytropic constant and $γ = C_{p} / C_{v}$ is the polytropic index.

Time stepping is forward Euler.

Variables it advances

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

Name	Kind	Accepted spaces
`fluid`	SPHVariable	`ParticlesSPH`

Options

Set these on the propagator in a parameter file, for example PushVinSPHpressure.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 density and pressure-force evaluation.
`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 velocity pushing.
`gravity`	`(0.0, 0.0, 0.0)`	tuple	Constant gravity vector added in the SPH pressure push.
`kappa`	`1`	float	Coefficient in the internal energy function.
`thermodynamics`	`isothermal`	`isothermalpolytropic`	Thermodynamic closure selecting the SPH pressure kernel.

Used by

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

ViscousEulerSPHFluidstep 3 of 4 · push_sph_p