Documentation of the main branch

These pages follow Mallard's main branch, which is ahead of release 0.8.0: some features they describe come with the next release.

Sources and sponges¶

Source terms add to the right-hand side per unit volume: gravity, body forces that hold a mass flow, arbitrary expressions, and sponge layers that damp the solution toward a reference state.

`[source]`¶

[source]
gravity = [0.0, -9.81]          # adds rho g to momentum, rho u.g to energy

Key	Default	Meaning
`gravity`	none	Gravitational acceleration vector
`mass_flow`	none	Hold the volume average of `rho u` at this vector with a uniform body force (periodic channels and pipes)
`rho`, `rhou`, `rhoE`	`"0"`	Mass, momentum (one expression per component) and energy sources, expressions of x, y, z, t
`time_dependent`	`false`	Re-evaluate the expressions at every Runge–Kutta stage (on the host: costly on large meshes); otherwise once at the start

Constant mass flow¶

A periodic channel has no inlet to fix its flow rate. mass_flow adds the uniform body force that keeps the volume-averaged momentum at the given value, correcting every stage so that a flow started at the target stays there to rounding; the energy gains the force's work.

# examples/channel_retau180: bulk density and velocity 1 along x
[source]
mass_flow = [1.0, 0.0, 0.0]

Gravity¶

Pitfall: the scheme is not exactly well balanced. A hydrostatic atmosphere carries spurious velocities of about 1e-4 of the sound speed on a 32 x 32 mesh, which vanish at second order under refinement; wall and symmetry ghost states continue the hydrostatic pressure gradient. The poiseuille_pipe example drives a pipe flow with gravity as a body force.

Sponge layers¶

[[sponges]] add -strength (U - U_ref) to the conservative variables (and species), damping the solution toward a reference state where the strength is nonzero. They absorb eddies and waves before an outlet, where characteristic conditions alone may reflect them or let reversed flow in.

Sponge strength rising quadratically over the last part of the domain

[[sponges]]
strength = "x > 4 ? 20 * ((x - 4) / 1)^2 : 0"   # 1/s; a gradual ramp reflects less than a step
u = [1.0, 0.0]
p = 1.0
T = 1.0

Key	Default	Meaning
`strength`	required	Damping rate [1/s], a number or an expression of x, y, z; zero outside the layer
`u`, `p`, `T`	required	Reference state, numbers or expressions of x, y, z
`X` or `Y`, `balance`	—	Mixtures: reference composition

Several sponges add up. Strength and reference are evaluated once, at cell centroids. The source is explicit and caps the time step at 1 / max(strength). Example: channel_inflow_retau180, a sponge over the last fifth of the channel in front of its nscbc_outlet.