Initial conditions

The optional top-level initial conditions section sets the displacement and velocity fields at t₀. It holds three lists: displacement, velocity, and traveling wave.

initial conditions:
  displacement:
    - node set: nsall
      component: z
      function: "0.001 * x"
  velocity:
    - node set: nsall
      component: x
      function: "100.0 * sin(pi * y)"

Each of the three keys must hold a list, even for a single entry. A scalar or mapping raises e.g. initial conditions.displacement must be a list.

Misspelled keys are reported

A typo in a list key warns:

[WARNING] Unknown key "velocities" in initial conditions. Did you mean "velocity"?

A typo in an entry key warns and then aborts, because the field it stands in for is required:

[WARNING] Unknown key "nodeset" in displacement IC entry 1. Did you mean "node set"?
ERROR: displacement IC entry 1 is missing required key "node set".
       Need: node set, component, function.

A typo in the section key (initial condition:) is caught by top-level validation, which warns the same way.

Carina releases before this behaviour left all three unvalidated, so a misspelling meant the initial condition was silently never applied and the run started from rest — indistinguishable from a physics result. If you are reading an older input file that behaved oddly, that is worth checking.

Displacement and velocity

Key	Required	Description
`node set`	yes	Exodus node set name.
`component`	yes	`x`, `y`, or `z`.
`function`	yes	Expression in `x`, `y`, `z`, `t`. See Function expressions.

Only free degrees of freedom receive initial values; DOFs constrained by a Dirichlet condition are skipped, and their values come from the boundary condition instead.

Integrator support

Integrator	`displacement`	`velocity`	`traveling wave`
`quasi static`	applied	ignored	ignored
`newmark`	applied	applied	applied
`central difference`	applied	applied	applied

Velocity and traveling-wave conditions are meaningful only to the dynamic integrators. Quasi-static runs drop them with a warning rather than an error:

[WARNING] Initial velocity ICs ignored for non-Newmark integrator.

The message says "non-Newmark"; it applies to any non-dynamic integrator, which in practice means quasi-static.

Traveling wave

A traveling-wave condition sets a displacement profile and the velocity field consistent with it propagating along an axis, without you having to write the derivative by hand.

initial conditions:
  traveling wave:
    - node set: nsall
      component: z
      displacement: "a=1.0e-3; s=0.1; a*exp(-(x-0.5)^2/s^2)"
      direction: x
      wave speed: 1000.0

Key	Required	Description
`node set`	yes	Exodus node set name.
`component`	yes	`x`, `y`, or `z` — the displaced component.
`displacement`	yes	Expression for the initial profile `u₀`.
`direction`	yes	Propagation axis: `x`, `y`, or `z`.
`wave speed`	yes	Signed speed `c`.

All five keys are required and validated; a missing one is a hard error naming the key, and direction must be x, y, or z.

Given u(x, t) = u₀(s − c t) with s the coordinate along the propagation axis, the consistent initial velocity is

v(x, 0) = −c · ∂u₀/∂s

Carina forms ∂u₀/∂s by symbolic differentiation of your displacement expression with respect to the direction axis, then evaluates both fields at t₀. There is no finite differencing and no automatic differentiation at initialization time.

wave speed is signed: the sign selects the direction of travel along the axis. Note that direction names the propagation axis while component names the displaced component — for a shear wave travelling along x and displacing z, use direction: x with component: z.

Application order

Conditions are applied in a fixed order:

displacement entries
velocity entries
traveling wave entries
initial acceleration solve
Dirichlet values propagated into the state

Traveling-wave conditions come after the plain lists deliberately, so that the derived velocity field overrides any zero-velocity default the earlier lists left in place. If a node appears in both a velocity entry and a traveling wave entry, the traveling wave wins.

At step 4 Carina solves for the initial acceleration. When the residual is already negligible it reports:

[SETUP]   Initial Acceleration = 0 (trivial RHS, ...)

which is informational, not an error.