DeepCausalityCFD

Blueprints

Couple thermochemistry to a compressible flow

The reentry sheath chain from gasdynamic jump through vibrational relaxation, finite-rate ionization and plasma frequency to comms cutoff, assembled as ordered stages over one marched field with a measured value at every link.

VibrationalLagStageFiniteRateIonizationStageRegimeClassifyBlackoutTrigger

The reentry sheath is the clearest multi-physics case in the crate. Five disciplines run over one marched field, each consuming the previous one’s output through a named scalar.

discipline              model                          publishes
─────────────────────────────────────────────────────────────────
compressible flow       Rankine–Hugoniot jump          T_tr, n_tot, pressure_atm
      ↓
vibrational relaxation  Landau–Teller, Millikan–White  T_ve, T_a
      ↓
finite-rate chemistry   RP-1232 three-channel network  alpha, n_e
      ↓
plasma electrodynamics  ω_p = √(n_e e² / ε₀ mₑ)        plasma_frequency
      ↓
link availability       ω_p > comms_band_rad_s         gnss_denied

Downstream of that, navigation degrades while gnss_denied holds, and the guidance decision is taken with the degraded state. Those two are covered in couple navigation to the physics stack.

The stages

From the corridor coupling stack, examples/avionics_examples/src/shared/world.rs:159-210:

    Coupling::between_steps()
        .then(
            VibrationalLagStage::new(
                utils::ft(T_VE_INITIAL),
                utils::ft(FALLBACK_PRESSURE_ATM),
                utils::ft(REDUCED_MASS_AMU),
                utils::ft(THETA_VIB),
                utils::ft(SHEATH_PEAK_AGE_S),
            )
            .with_pressure_field("pressure_atm"),
        )
        .then(
            // The finite-rate network reads "T_tr" and "T_ve" directly and
            // builds each channel's controlling temperature internally; there
            // is no Saha calibration target anywhere in this stage.
            FiniteRateIonizationStage::new(utils::ft(FALLBACK_N_TOT))
                .with_density_field("n_tot")
                .with_sheath_renewal(utils::ft(SHEATH_PEAK_AGE_S)),
        )
        .then(FreestreamFeeds)
        .then(RegimeClassify::new(utils::ft(L_CHAR), utils::trigger()))

The handoff is by field name, through CoupledField.

VibrationalLagStage reads T_tr and an optional per-cell pressure field, and writes two scalars: T_ve, the lagged bath, and T_a = √(T_tr·T_ve), Park’s rate-controlling temperature. It relaxes from the frozen free-stream value over one residence time rather than integrating the carried T_ve over dt, which is the parcel-renewal picture for a continuously refreshed sheath.

FiniteRateIonizationStage reads T_tr and T_ve and builds each channel’s controlling temperature internally: ionization at the geometric mean, dissociation at Park’s T_tr^0.7·T_ve^0.3, electron channels at T_e = T_ve. It writes alpha and n_e. The network is reversible, carrying dissociative recombination as well as forward ionization, which is the mechanism that ends the blackout.

RegimeClassify reads the peak of n_e and converts it to a plasma frequency and a denial flag.

Ordering is load-bearing. A stage placed before its input exists reads the previous step’s value.

The field registry is by convention

These keys have no declared constant list. Each is a &'static str struct field defaulted in the stage’s new(), with an opt-in override such as with_pressure_field or with_density_field. The producer side is a bare literal in the carrier, compressible_march_run.rs:441-444:

        field.set_scalar("speed", speed);
        field.set_scalar("T_tr", t_tr);
        field.set_scalar("n_tot", n_tot);
        field.set_scalar("pressure_atm", p_atm);

The backing store is an association list, Vec<(String, Vec<R>)>, with linear scan. Two consequences matter in practice.

A missing key is a silent no-op. Every stage opens with let Some(x) = field.scalar(..) else { return Ok(()) }, so a misspelled field name disables that stage without an error.

A wrong-length key is a hard error. The shape contract is checked, so a field present at the wrong cell count fails the step.

The stagnation-line target reports the whole chain in one artifact. deep_causality_cfd/verification/qtt_ramc_stagline/baseline.txt:

Exact Rankine–Hugoniot post-shock state (the transported energy, no reconstruction):
  T_inf -> T2 ............ 250 K -> 8044 K
  density ratio ρ2/ρ1 ... 20.349
  velocity ratio u2/u1 .. 0.049
  pressure ratio p2/p1 .. 6.547e2
  post-shock n_tot ...... 2.645e22 m^-3

Stagnation-line blackout (Saha/Park-2T at the post-shock state):
  ionization fraction α .. 2.007e-5
  peak electron density .. 5.310e17 m^-3
  plasma frequency ω_p ... 4.111e10 rad/s
  blackout (ω_p > comms) . true (comms band 9.40e9 rad/s)
  relaxation-profile bond  2  (smooth post-shock zone, O(1) rank)

The chain closes. α · n_tot gives 5.310e17 m⁻³ against the reported n_e, and √(n_e e²/ε₀mₑ) gives 4.111e10 rad/s against the reported ω_p, both to better than 0.1%. The plasma frequency exceeds the configured threshold by a factor of 4.4.

The closed-form Park-2T controller lands at 5.310e17 m⁻³, 1.27 decades below the RAM-C II flight anchor of ~1e19 m⁻³, after the N₂–N₂ reduced-mass correction (μ = 14.007; the former near-anchor landing came from an invalid μ = 7.0). See validation status for that offset and for the uncalibrated finite-rate network, which lands within +0.35 decade of the anchor.

Coupling direction

Chemistry to flow is absent by construction. The step order is advance then coupling.apply (carrier.rs:126-131): advance produces the next conserved state from the conserved state alone, and the coupling runs afterwards and mutates only the CoupledField. Across the whole carrier the only scalar read back out of the field is truth_state. The coupling carries no chemical energy sink, no electron-pressure term, and no density or energy feedback.

The EosStage doc states the same limit: the marcher does not consume the pressure closure it writes.

Trajectory and flow do form a closed loop. BankSteeredLift writes an aero force into the field’s force channel; TrajectoryNav consumes it as the propagator kick and republishes the vehicle state; the descent schedule evaluates the atmosphere at that state and sets the inflow strip for the next step. Navigation feeds flow, and flow feeds navigation.

Because the chemistry never modifies the flow, the plasma state has no influence on the vehicle’s trajectory. n_e acts only on the GNSS-denial gate applied to the ESKF correction. Blackout degrades the estimate, not the truth.

That path from bank command to flow exists through the trajectory, so the following is a magnitude result rather than a structural one. Across the corridor’s seventeen bank branches the flow columns are invariant to three significant figures while the trajectory outcome varies by nearly a factor of ten:

Column Range across 17 branches
Peak heat flux 2.232e6 to 2.240e6
Thermal load 1.459e7 to 1.460e7
Peak n_e 6.224e19 to 6.309e19
Miss distance 20.000 m to 2.070 m

Over the branch continuation window the bank command does not move the sampled atmosphere enough to alter the shock-layer chemistry at three digits. The branches diverge by decision rather than by flow.

The retropulsion descent is the closest case to a two-way chemistry coupling, and it stops short of one. Its PlumeImprint seam gives the marched layer state realism, but in-flight drag authority is the cited A0 correlation rather than a decrement contracted from the evolved field. The de-risk measurement behind that choice is recorded on capability boundaries.

Regime as a coupled observable

gnss_denied is not a schedule. BlackoutTrigger::evaluate maps the peak electron density through the plasma-frequency kernel and applies a strict comparison against a single configured angular threshold, comms_band_rad_s. Both sides are in rad/s, so no 2π conversion appears. The blackout window is therefore an output of the chemistry. The corridor records the transitions:

regime -> slip (GNSS-available), Kn=0.07829109848665225
regime -> slip (GNSS-denied), Kn=0.012690837165407727
regime -> continuum (GNSS-denied), Kn=0.00993838892165156
regime -> continuum (GNSS-available), Kn=0.0002551442196046344

Two independent axes move here. The Knudsen number crosses the slip-continuum band as density rises; the comms state crosses in and out of denial as the sheath forms and recombines. They are not synchronised, and the classifier tracks them separately. See detect and act on a regime change.

Applicability limits

The corridor closure is single-point with T_e = T_ve lumped, and there is no spatially resolved reacting layer. The stagnation-line target adds the fitted shock interface and the transit-age profile.

Reported peak n_e is sensitive to the model choice. The closed-form Park-2T controller path lands 1.27 decades below the anchor after the N₂–N₂ reduced-mass correction; the uncalibrated finite-rate network lands at +0.35 decade (~2.25×), inside a ±0.70 decade band earned from the measurement. The T_e = T_ve lumping is worth roughly 2×, and the documented chemistry-model spread is 2× to 5×.

γ = 1.1 is an effective-γ closure chosen so the post-shock temperature lands near 8000 K. Perfect gas at γ = 1.4 over-predicts T₂ at roughly 30 000 K.

Worked examples using this