Component index — model · theory · example · tutorial

This is the single cross-reference for every component aeolus1d models. Each row links the four things you usually want together but that otherwise live on separate pages:

• Model used — the physics/numerics, named, with the key reference. Full citations are in the linked theory section.
• Theory — the equations, in Theory.
• Prose / fields — the narrative closure write-up in Closures, and the field-level dispatch table in Closures — reference (lists the exact TOML keys each kind consumes).
• Example — a self-contained runnable examples/*.toml (run with aeolus1d run examples/<file>); plot scripts mirror each by index in examples/plots/.
• Tutorial — a guided walkthrough, where one exists.

If you are new, read the Tutorials first — they walk the pipeline end-to-end. This page is the lookup you come back to when you need "where is component X documented, and what's a working case I can copy?".

How the columns map to the solver pipeline

The sections below follow the order data flows through a run: initial/geometry → spatial scheme → EOS → source closures → species & reactions → boundary conditions → network coupling → engine components → controllers → vehicle system → learned seams. The same order the runtime uses in Runtime data flow.

---

1. Initial conditions & geometry

Component (kind)	Model used	Theory	Example
Initial field — uniform / riemann / regional / mode	Direct primitive-state init; Riemann = left/right discontinuity at x0	§1.1 Quasi-1D Euler	01_single_pipe_sod.toml
Area profile — parabolic / tanh_step / tabulated	Quasi-1D area-source term A(x)	§2.1 Finite-volume discretisation	02_cd_nozzle.toml

→ Tutorial: Sod shock tube.

2. Spatial scheme & flux (core numerics)

Component	Model used	Theory	Example
Reconstruction — 1st-order / MUSCL / MP5	MUSCL-Hancock slope-limited; MP5 (Suresh-Huynh) 5th-order	§2.2 Spatial reconstruction	23_mp5_sod.toml
Riemann flux — HLLC / HLLC-LM	HLLC (Toro); HLLC-LM low-Mach fix (Thornber)	§2.3 Riemann solver	24_hllc_lm_pulse.toml
Time integration — SSP-RK / implicit-Euler / BDF2 / Radau	Explicit SSP-RK2/3; implicit block-Thomas Newton with Phase I-Y Picard outer loop (adaptive_picard)	§2.4 Time integration, Numerics, Implicit-solver reference	40_implicit_adaptive_pipe.toml, 54_adaptive_picard_turbo.toml, 57_picard_stiffness_step.toml

3. Equation of state

Component (kind)	Model used	Theory & prose	Example
EOS — ideal	Ideal gas p = ρRT	§1.2 EOS · Closures: Gas EOS	most examples
EOS — redlich_kwong / peng_robinson	Cubic real-gas with closed-form analytic Jacobians	§1.2 EOS · Closures: real-gas Jacobians	09_real_gas_shock_tube.toml, 17_real_gas_nozzle.toml, 18_real_gas_catalyst.toml, 19_real_gas_plenum.toml
EOS — tabulated	CoolProp-tabulated (T, ρ)→(p, e, ∂p/∂T, ∂p/∂ρ) panel, built at build_network time	§1.2 EOS	58_tabulated_eos_implicit.toml

Notes: EOS is per-pipe — [pipe.eos] R_gas overrides [gas] R_gas so each pipe can carry a different working fluid. Real-gas/tabulated sound speed uses the local cv_real = ∂e/∂T|_ρ (ideal cv plus the departure term), not the scalar reference cv.

4. Source-term closures

Family (kinds)	Model used	Theory · prose · fields	Example
Friction — darcy_const / colebrook / minor_loss	Darcy-Weisbach; Colebrook-White ε/D; bend & minor-loss K	§3.1 Friction · prose · fields	77_pipe_flow_heat.toml, 78_pipe_bend_loss.toml, 79_orifice_plate.toml, 81_bend_geometric.toml
Wall heat — constant_twall / egr_cooler / charge_air_cooler / flow_nu	Fixed-h; ε-NTU heat-exchanger; Nusselt-correlation convective	§3.2 Wall heat transfer · prose · fields	44_egr_cooler.toml, 75_coolant_pipe.toml, 80_pipe_wall_warmup.toml, 82_multilayer_wall.toml
Porous — darcy_forchheimer / _kc	Darcy-Forchheimer (α/β or K/C_F) + Sutherland μ	§3.3 Porous media · prose · fields	05_catalyst_plug.toml (substrate)
Catalyst — two_phase_heat / _var_nu / mechanism	Two-phase solid/gas energy, h·a_v·(T_s−T_g), var-Nusselt	§3.4 Two-phase catalyst · fields	05_catalyst_plug.toml, 07_catalyst_thermal_front.toml, 18_real_gas_catalyst.toml
Particulate filter — diesel_particulate_filter	Cake Δp (Konstandopoulos), soot load, NO₂/active regen	Closures: Aftertreatment · fields	41_dpf_regen.toml, 49_dpf_no_inhibition.toml, 50_dpf_active_regen.toml, 55_dpf_regen_hrr.toml, 56_dpf_regen_lowmach.toml, 84_dpf_substrate_inertia.toml
DPF solid thermal mass — [pipe.filter.thermal]	Per-cell cake T_cake, substrate-wall thermal inertia, canning loss to ambient	fields	84_dpf_substrate_inertia.toml, 55_dpf_regen_hrr.toml
Catalysed soot filter — [pipe.filter.csf]	Arrhenius CO + C₃H₆ oxidation on the washcoat, with mass-transfer-limited rate caps	fields	41_dpf_regen.toml (passive by default)
Coolant coupling — [[coolant_coupling]]	Cell-aligned gas-pipe ↔ coolant-pipe exchange through a dynamic wall	fields	75_coolant_pipe.toml, 44_egr_cooler.toml

→ Tutorial: Aftertreatment chain. ADRs: ADR-0005 catalyst energy coupling.

5. Species transport & reactions

Operator-split (Strang) chemistry — see §7 Strang-split chemistry, §3.5 Species transport, and ADR-0001 operator-split stiff chemistry. Field-level table: Closures — reference: family reaction.

Reaction kind	Model used	Example
arrhenius_scr_demo / _multi_demo	Single/multi-species Arrhenius demo	08_reactive_pipe.toml, 21_multi_species_kinetics.toml
nh3_ads_des	NH₃ adsorption/desorption storage (Temkin α_des)	42_scr_urea_injector.toml
nh3_scr_kinetics	Standard + fast SCR + NH₃ oxidation kinetics	42_scr_urea_injector.toml, 45_two_stage_scr.toml, 38_engine_turbo_scr.toml
nh3_slip_catalyst	Ammonia-slip catalyst (SCR + selective ox)	43_scrf.toml
hc_oxidation / doc_oxidation / doc_oxidation_voltz	HC/CO oxidation; Voltz self-inhibition kinetics	46_doc.toml
doc_oxidation_S	DOC + sulfur poisoning coverage θ_S	61_doc_sulfur_poisoning.toml
twc / twc_brinkmeier	Three-way catalyst; Brinkmeier O₂-storage (OSC)	74_twc.toml (OSC demo + plot); avl_cruise_m/c02012_gasoline.toml (twc); validation/heliyon_twc_co_oxidation/case_co2_production_300C.toml (twc_brinkmeier)
hnco_hydrolysis	HNCO → NH₃ urea-decomposition branch	48_hnco_hydrolysis.toml
mechanism	Spec-driven mass-action mechanism (mechanism_file, TOML/YAML) compiled to py_reaction_multi	35_mechanism_pipe.toml, examples/mechanisms/
Multi-species transport	Y + Y_extras canonical layout	20_multi_species.toml
Per-cell variable γ	γ(T, Y) built from species NASA-7 thermo → variable-γ HLLC (Karni); [pipe.species] per_cell_gamma (default off), gamma_T_from_energy (default on — energy-consistent T recovery, γ-contact pressure-preserving), caloric_thermo (default on since 2026-08-06 — inverts the true e = ∫c_v dT instead of the calorically-perfect e = c_v(T)·T, worth −105 K at 1000 K; inert unless per_cell_gamma is set)	87_multicomponent_variable_gamma_shock_tube.toml

Integrators: §7 — LSODA (15_strang_chemistry.toml) vs. @njit Bader-Deuflhard BS (16_bs_chemistry.toml). ADR-0003 canonical extras layout, ADR-0004 implicit-upwind QS species, ADR-0009 inflow-ghost species conservation. → Recipes: Aftertreatment chain, Train an ML chemistry surrogate. → Authoring a custom mechanism or adding a species: Chemistry file formats. → Thermo data for a species the seed DB lacks: aeolus1d thermo-db fetch pulls Burcat's ~3700-species NASA-7 database to a user-local cache (not bundled — it is non-commercial-use only, and aeolus1d is MIT). See Chemistry file formats — Burcat's database and CLI — aeolus1d thermo-db.

6. Boundary conditions

Theory: §4 Boundary conditions. Fields: Closures — reference: BC.

BC kind	Model used	Theory	Example
wall / transmissive	Reflecting wall / zero-gradient outflow	§4.1	01_single_pipe_sod.toml
stagnation_inlet / pressure_outlet	Isentropic stagnation in; static-p out	§4.2, §4.3	02_cd_nozzle.toml
nonreflecting	LODI / Poinsot-Lele characteristic	§4.4	22_lodi_port.toml
transient_* (stagnation / pressure / mass-flow / velocity)	Time-tabulated BC schedules, incl. species	§4.5, §4.8	04_pulsed_intake.toml
valve_inlet / valve_orifice	Cam-lift inlet; Winterbone-Pearson orifice flow	§4.6	25_valve_inlet.toml, 26_valve_orifice.toml
mass_flow_inlet / velocity_inlet	Prescribed ṁ or u with T0	§4.7	—
egr_valve / throttle	Orifice valve with supply-gas composition	§4.6	72_throttle_demo.toml, 62_egr_valve_ctrl.toml

7. Network coupling (junctions)

Theory: §5 Network coupling. Picard outer loop: Implicit network — Picard.

Junction kind	Model used	Theory	Example
plenum	0-D mass + energy ODE volume	§5.1	03_two_pipes_junction.toml, 11_neck_pipe_junction.toml
corberan	Corberán CP+h pressure-loss junction	§5.2	12_cp_junction.toml, 10_cp_junction_kloss.toml
ehr	Extended Helmholtz Resonator (per-port u_n ODE)	§5.3	13_ehr_helmholtz.toml
passthrough / biased_plenum	Inline pass; biased AdBlue distributor plenum	§5.1	42_scr_urea_injector.toml
Quasi-2D plenum	Spatially-resolved Helmholtz volume	§5.4	06_helmholtz_quasi2d.toml

→ Tutorial: Networks and junctions.

8. Engine components

Theory: §6 Engine components.

Component	Model used	Theory	Example
Reciprocating cylinder	Slider-crank volume; compressible-orifice valve coupling; well-mixed charge composition + complete-combustion products	§6.1, ADR-0008, field reference	31_cylinder.toml, 50_two_cyl_engine.toml, 91_cylinder_species_transport.toml
Wiebe combustion	Single/multi-Wiebe heat-release; knock retard	§6.2	52_knock_event.toml
Compressor / turbine	Quasi-steady map-driven; shared-shaft turbo	§6.3 · surge/choke	27_compressor.toml, 28_turbo_shaft.toml, 83_turbo_robustness.toml
VGT / sequential turbo	3-D vane-axis map; twin-sequential; wastegate	§6.3	55_vgt_3d_turbo.toml, 59_wastegate_boost_ctrl.toml, 60_twin_sequential_turbo.toml
Variable valve timing	Cam-phase shift (Phase E5)	§6.4	(engine cases)
Full engine chain	Cylinders → turbo → aftertreatment → tailpipe	§6	39_4cyl_engine_turbo_scr.toml, 71_ktm_510_si.toml

→ Tutorial: Engine end-to-end · Post-processing.

9. Closed-loop controllers

Prose: Closures: Closed-loop controllers.

Controller	Model used	Example & recipe
Throttle PI	Manifold-pressure feedback	72_throttle_demo.toml → recipe
EGR + O₂ feedback	EGR-valve closed loop on O₂	62_egr_valve_ctrl.toml → recipe
VGT / wastegate boost	Boost-pressure PI	51_vgt_boost_ctrl.toml, 59_wastegate_boost_ctrl.toml
Spark / knock retard	Spark-timing & knock controllers	63_spark_timing_ctrl.toml, 52_knock_event.toml
DPF heater	Active-regen PI on cake temperature	53_dpf_heater_ctrl.toml

10. Vehicle system / drive cycles

Component	Model used	Doc	Example
Drive cycle	Vehicle longitudinal dynamics, gear/road load	Vehicle system	85_vehicle_drive_cycle.toml, 76_wltp_lite_dpf.toml
Electrified drive cycle	Parallel-hybrid engine/e-motor torque split, coulomb-counted battery SoC	Vehicle system	86_electrified_drive_cycle.toml

Vehicle drive-cycle cases run with aeolus1d drive-cycle <file> --out trace.csv (the self-contained cycle path), not aeolus1d run.

11. Learned / ML seams

Pattern: Closures: ML substitution pattern.

Seam (kind)	Model used	Example & recipe
Junction BC — learned_npz	NN port-state surrogate	14_py_junction_bc.toml, 29_learned_junction_bc.toml
Turbo map — learned_npz	NN compressor/turbine map	30_learned_turbo_map.toml
Surface-chemistry surrogate	NN reaction-rate surrogate	→ recipe

---

Not on this page

A few subsystems are documented but aren't per-component rows:

• Inverse problems / [optimize] — fitting model parameters to data: §9 Inverse problems, examples/optimize/.
• Acoustic mode analysis — Helmholtz + FEM eigensolver + state-space linearization: §8 Acoustic mode analysis, Mode analysis.
• Run / case settings — every [case] / CaseHeader field: Run settings.
• Import from AVL Cruise M / GT-Suite — Interop, examples/avl_cruise_m/.
• Validation suites — paired with published/proprietary data: Validation dossier, examples/validation/.
• Driving from Python — the load_case → build_network → run_case / dispatch_advance call surface, the Pipe state you read in a sampler, and the closure registry: API reference.