flow.EnergyConfig

flow.EnergyConfig(
    shape,
    fluid_diffusivity,
    conductivity_ratio=200.0,
    inlet_temperature=0.0,
    wall_temperature=None,
    scheme='exponential',
    tol=1e-10,
    max_steps=4000,
    restart=60,
)

Static settings for one conjugate energy solve.

Attributes

Name	Type	Description
shape	tuple[int, int, int]	`(NX, NY, NZ)` lattice, duct axis along `+Y`, matching the momentum solve’s grid exactly.
fluid_diffusivity	float	The air’s thermal diffusivity in lattice units, `nu / Pr`. Numerically also its conductivity, because `(rho cp)_f` is the unit of this system.
conductivity_ratio	float	`k_solid / k_fluid`. Aluminium in air is about 8000; a ratio that large is physically right and numerically punishing (see the module docstring on conditioning), so a study that only needs “much better than air” is better served by a few hundred.
inlet_temperature	float	Temperature carried in at the inlet plane.
wall_temperature	float \| None	Temperature of the duct’s lateral walls, or `None` (the default) for adiabatic walls — the right choice for a duct that is not itself a heat exchanger.
scheme	str	`"exponential"` or `"upwind"`; see the module docstring.
tol	float	Relative residual the linear solve stops at.
max_steps	int	Iteration cap for the linear solve.
restart	int	Krylov subspace size before GMRES restarts, and the one setting here that can silently return a wrong answer. Restarted GMRES stagnates when the subspace is too small for the operator’s spectrum, and the conductivity ratio is what sets that spectrum: on a 14x26x14 duct, `restart = 30` converges to 2.9e-12 at a ratio of 50 and stalls at a relative residual of 0.23 at a ratio of 200 – reporting a peak temperature of 0.014 where the answer is 0.602, with no error and no warning. 60 converges at both. It costs `restart` stored fields, which is the reason not to simply set it very high on a large lattice. :func:`energy_imbalance` is the check that catches a stall, and :attr:`~cadjoint.flow.study.FlowStudyResult.warnings` runs it.

Raises

Name	Type	Description
	ValueError	On a non-positive diffusivity or conductivity ratio, or an unknown scheme.