Namespaces
namespace	numeric
namespace	units

Classes
class	CanteraThermo
	ThermoAccessor backed by a PlasmaPhase. More...
class	ChannelCircuit
	The channel side of the circuit coupling. More...
struct	ChannelHistory
struct	ChannelOptions
struct	CircuitSample
	The circuit columns of one recorded frame. More...
class	CollisionModel
	Composition-resolved electron-heavy momentum-transfer collision model. More...
struct	ColumnOptions
	Solver configuration. All fields have defaults matching a typical H2 arc. More...
struct	ColumnResult
	Output of a completed column solve. More...
class	DruyvesteynRate
struct	ElectronReactionIndex
	The per-reaction data the electron pool's inelastic power needs. More...
struct	ElectronTemperatureData
	Shared data carrying the electron temperature (mirrors Cantera's own TwoTempPlasmaData but only needs Te). More...
class	GammaLawThermo
	Calorically perfect ideal-gas accessor: one constant \(\gamma_\mathrm{H}\) for the heavy pool, ElectronGamma for the electron pool. More...
struct	HydroStepConfig
	Geometry, boundary treatment and stepping controls for one call. More...
struct	HydroStepResult
	Diagnostics from one call, enough to assert NUMERICS.md section "Positivity under a strong rarefaction", case 19, without re-deriving the sub-cycling in the test. More...
struct	HydroStepState
	Per-node primitive state, advanced in place. More...
class	JanevDissociativeRecombinationC2HyRate
struct	NodeState
	Primitive state at one radial node, as the ghost-state callback sees it and returns it. More...
class	PlasmaCell
	Shared single-cell two-temperature reacting-plasma RHS (one physics source). More...
struct	PlasmaCellConfig
class	PlasmaChannel1D
	Transient, two-temperature (Te != Tg), finite-rate reacting 1-D radial plasma channel (custom Cantera Domain1D). More...
struct	PlasmaChannelConfig
	Everything PlasmaChannel1D needs to build itself. More...
class	PlasmaReactor0D
	Native C++ two-temperature 0D plasma reactor (stateless per-eval evaluator). More...
struct	PlasmaReactor0DConfig
class	PrescribedPressureThermo
	Pressure prescribed as a function of (r, t), every other property delegated to a GammaLawThermo. More...
class	PropertyTable
struct	RadialDiffusionCoefficients
	Everything the diffusion block needs that the grid and the state do not carry: the transport coefficients, the wall ghost, and the per-species properties the two energy terms close with. More...
struct	ReverseTwoTempData
	Shared data for all reverse-two-temperature-plasma reactions. More...
class	ReverseTwoTemperaturePlasmaRate
	Reverse of a forward two-temperature-plasma reaction: More...
struct	StateProperties
	Every state function hydroStep() reads off one primitive state when it builds the conservative variables, returned together by ThermoAccessor::stateProperties(). More...
class	ThermalPlasmaColumn1D
	Steady radial LTE Elenbaas-Heller arc column (custom Cantera Domain1D). More...
class	ThermoAccessor
	Equation-of-state and caloric accessor injected into hydroStep(). More...
class	TrialStateError
	A state the closures cannot evaluate: a temperature outside the fits, an undefined Coulomb logarithm, or a non-finite rate. More...
struct	TwoTemperatureState
	The two-temperature equation of state at the state currently set on a phase, PHYSICS.md (G6). More...
struct	WallEnergyOutflow
	Energy leaving through the wall ghost face per unit time, per unit axial length and per radian [W/m] – the convention of V_cell and of HydroStepResult::boundary_total_energy_out. More...

Typedefs
using	GhostStateFn
	Fill the outer ghost cell from a closed-form solution, a fixed end state, or a mirror of the interior.

Enumerations
enum class	OuterBc { AmbientGhost , PressureOutlet }
	Outer-boundary treatment (NUMERICS.md section 7). More...

Functions
bool	equationHasElectron (const std::string &equation, const std::string &electron)
	Test whether the electron participates in a reaction equation as a standalone token.
ElectronReactionIndex	buildElectronReactionIndex (Cantera::Kinetics &kinetics, const std::string &electron, const std::vector< double > &species_h0k, std::size_t n_species, bool reacting)
	Build the index for one mechanism.
std::shared_ptr< Cantera::Solution >	loadMechanism (const std::string &mech, const std::string &phase)
	Load a mechanism with rizer's custom rate types registered first.
void	registerPlasmaRates ()
	Register the custom plasma reaction rates with Cantera's ReactionRateFactory.
OuterBc	parseOuterBc (const std::string &mode)
	Map an outer_bc_mode config string onto the enum.
HydroStepResult	hydroStep (const HydroStepConfig &cfg, HydroStepState &state)
	Advance state over one Strang half-step of cfg.dt_total.
ChannelHistory	solveChannelTransient (const ChannelOptions &opts)
	Build a PlasmaChannel1D from opts.cfg, advance it from t=0 to \(t = \mathtt{opts.dt} \cdot \mathtt{opts.n\_steps}\) [s] with the stiff BDF backend, and return the recorded radial history.
void	addRadialDiffusion (const PlasmaChannel1D &domain, Cantera::span< const double > x, const RadialDiffusionCoefficients &c, std::size_t j, double lhsTg, double lhsTe, double &dTg, double &dTe, double dYdt, double scratch)
	Add one node's diffusive contributions to the rates the caller holds.
WallEnergyOutflow	wallEnergyOutflow (const PlasmaChannel1D &domain, Cantera::span< const double > x, const RadialDiffusionCoefficients &c, const double *species_enthalpy)
	What conduction and species diffusion move through the wall face at the state x.
ColumnResult	solveColumn (double R, double electric_field, double T_wall, const PropertyTable &sigma, const PropertyTable &kappa, const PropertyTable &p_rad, const ColumnOptions &opts)
	Build, solve, and extract the radial Elenbaas-Heller column.
std::string	significant (double value)
	`value` to 6 significant digits, for exception messages.
void	throwOutsideTable (const PropertyTable &table, double x, const char procedure, const std::string &what, const char unit, const char *remedy)
	Throw the TrialStateError for `x` outside `table`.
double	evalAtState (const PropertyTable &table, double x, const char procedure, const char what, const char unit, const char remedy)
	Value of `table` at `x`, refused outside its tabulated range.
double	monatomicElectronCv (double electron_molecular_weight)
	Electron specific heat at constant volume, per kg of ELECTRONS, \(c_{v,\mathrm{e}}=\tfrac32 R/W_\mathrm{e}\).
TwoTemperatureState	readTwoTemperatureState (const Cantera::PlasmaPhase &phase)
	Read the two-temperature EOS back from a phase whose state is set.

Variables
constexpr double	TemperatureFloor = 200.0
	Lower limit of the mechanism's NASA polynomials [K].
constexpr double	TemperatureCeiling = 1.0e5
	Upper limit of the physically meaningful range [K].
constexpr double	GasConstant = units::R_kmol
	Universal gas constant [J/kmol/K] and Boltzmann's constant [J/K], from units.h rather than Cantera's CODATA-2018 values, to match the Python reactor reference this extension is a port of.
constexpr double	Boltzmann = units::k_b
constexpr double	ElectronGamma = 5.0 / 3.0
	Ratio of specific heats of the electron pool [-].

Typedef Documentation

◆ GhostStateFn

using rizer::GhostStateFn

Initial value:

std::function<NodeState(

double r_ghost, double t, bool is_inner_face, const NodeState &interior)>

rizer::NodeState

Primitive state at one radial node, as the ghost-state callback sees it and returns it.

Definition BoundaryConditions.h:25

Fill the outer ghost cell from a closed-form solution, a fixed end state, or a mirror of the interior.

TEST-ONLY, unset in production, and overriding outer_bc_mode when set.

It takes the adjacent interior state as well as the ghost radius and the time because the validation cases need three different things from it and only the first is a closed-form field (NUMERICS.md section 7).

r_ghost is the GHOST CELL's own node radius – the adjacent interior node reflected across the boundary – and not the face radius. A closed-form field sampled at the face would land half a cell inside the ghost it fills, which is an O(1) error in the boundary cell that refinement does not remove (NUMERICS.md section 7.6). hydroStep() hands the same radius to the thermo accessor for that ghost, so a prescribed pressure and a prescribed state are sampled at one consistent place.

is_inner_face distinguishes the two ends. NUMERICS.md section 7 gives the signature as (r, t, W_interior), which is enough in cylindrical mode where the inner face has zero area and is never consulted – but the planar entry point of section "Full system, planar - Sod shock tube" has two real boundaries at the same face radius (r_face = 1 everywhere), and cases 14 and 15 need a different end state at each. The inner face is consulted only when r_face[0] > 0, i.e. exactly when it has nonzero area.

Definition at line 89 of file BoundaryConditions.h.

Enumeration Type Documentation

◆ OuterBc

enum class rizer::OuterBc

strong

Outer-boundary treatment (NUMERICS.md section 7).

Two values only: the closed-form boundary the validation cases need arrives through HydroStepConfig::ghost_state, deliberately not as a third enum value a production config could select.

Enumerator

AmbientGhost

Fix rho, u_r, p, T and Y_s to ambient.

The DEFAULT, and the accurate choice whenever R_max is placed beyond the front so that the far field genuinely IS the ambient state: the characteristic count says only one quantity MAY be imposed when the others are unknown, and imposing values that happen to be the true ones costs nothing. It both transmits an outgoing wave and anchors the domain to ambient, which nothing else here does (NUMERICS.md sections 7 and 11.8).

PressureOutlet

Hold p = p_amb at the boundary face, extrapolate u_r/Tg/Te/Y_s with zero gradient, and close rho from the equation of state at that p_amb.

Exactly one quantity imposed – and REFLECTING for all that, because pinning p is a pressure-release surface. Measured at 0.33 to 0.62 of an incident wave against AmbientGhost's 0.013 to 0.024, and it rings instead of settling. Kept as a documented comparison point, not as a treatment to reach for.

Definition at line 37 of file BoundaryConditions.h.

Function Documentation

◆ addRadialDiffusion()

void rizer::addRadialDiffusion	(	const PlasmaChannel1D &	domain,
		Cantera::span< const double >	x,
		const RadialDiffusionCoefficients &	c,
		std::size_t	j,
		double	lhsTg,
		double	lhsTe,
		double &	dTg,
		double &	dTe,
		double *	dYdt,
		double *	scratch )

Add one node's diffusive contributions to the rates the caller holds.

Reads the state at \(j-1\), \(j\) and \(j+1\), so it reaches outside the [jmin, jmax] window its caller loops over – the stencil is what makes the Jacobian banded, and the neighbours are read, never written.

Parameters

[in]	domain	Grid and state layout: z(), faceRadius(), faceSpacing(), index() and the per-node density
[in]	x	This domain's state vector
[in]	c	Coefficients and ghosts, see above
[in]	j	Node to evaluate [-]
[in]	lhsTg	Heavy-pool capacitance [J/m^3/K]
[in]	lhsTe	Electron capacitance [J/m^3/K]
[in,out]	dTg	Heavy-pool rate, added to [K/s]
[in,out]	dTe	Electron rate, added to [K/s]
[in,out]	dYdt	Species rates, added to [1/s], length K
[out]	scratch	Caller-owned workspace, length K; holds \(\nabla\cdot(\rho D\nabla Y_s)\) on return

Definition at line 149 of file RadialDiffusion.cpp.

◆ buildElectronReactionIndex()

ElectronReactionIndex rizer::buildElectronReactionIndex	(	Cantera::Kinetics &	kinetics,
		const std::string &	electron,
		const std::vector< double > &	species_h0k,
		std::size_t	n_species,
		bool	reacting )

Build the index for one mechanism.

species_h0k is required only when the mechanism has an electron-impact reaction and chemistry is live: without it the inelastic power would be silently zero, which is why this raises rather than defaulting.

Parameters

[in]	kinetics	The mechanism's kinetics
[in]	electron	Electron species name
[in]	species_h0k	Per-species formation enthalpy at 0 K [J/kmol], length nSpecies(), or empty when reacting is false
[in]	n_species	Expected length of species_h0k [-]
[in]	reacting	Whether finite-rate chemistry is live [-]

Returns: The index above

Exceptions

std::invalid_argument if species_h0k is missing or the wrong length while an electron-impact reaction is live

Definition at line 36 of file ElectronReactions.cpp.

◆ equationHasElectron()

bool rizer::equationHasElectron	(	const std::string &	equation,
		const std::string &	electron )

Test whether the electron participates in a reaction equation as a standalone token.

Replaces the reaction-arrow and stoichiometric-plus characters +, =, <, > with spaces and looks for the electron as a whole token, which is what makes a spectator electron count: Cantera cancels it from the stoichiometry, but it is still an electron-impact reaction.

Parameters

[in]	equation	Reaction equation, e.g. "CH4 + e- => CH3 + H + e-"
[in]	electron	Electron species name as the mechanism spells it

Returns: True when the electron appears as its own token

Definition at line 17 of file ElectronReactions.cpp.

◆ evalAtState()

double rizer::evalAtState	(	const PropertyTable &	table,
		double	x,
		const char *	procedure,
		const char *	what,
		const char *	unit,
		const char *	remedy )

inline

Value of table at x, refused outside its tabulated range.

Parameters

[in]	table	Table to evaluate, not empty
[in]	x	State variable to evaluate at [units of the abscissa]
[in]	procedure	Function evaluating it, for the exception
[in]	what	Name of the tabulated property, for the exception
[in]	unit	Unit of the abscissa, for the exception
[in]	remedy	What the caller can change to cover the state

Returns: The interpolated value

Exceptions

TrialStateError if x is outside [table.first(), table.last()]

Definition at line 50 of file TableLookup.h.

◆ hydroStep()

HydroStepResult rizer::hydroStep	(	const HydroStepConfig &	cfg,
		HydroStepState &	state )

Advance state over one Strang half-step of cfg.dt_total.

Internally, PER CFL SUB-CYCLE and not once per call: primitive to conservative, Rusanov fluxes plus the cylindrical geometric momentum source, forward Euler, then conservative back to primitive through the energy inversion of NUMERICS.md section 8. The round trip sits inside the sub-cycle loop because every sub-cycle's fluxes and sources need a current p; hoisting it out would freeze the pressure gradient driving the rarefaction, which is the one quantity an explicit acoustic step cannot hold fixed.

Parameters

[in]	cfg	Geometry, boundary treatment, stepping controls and the injected thermo accessor
[in,out]	state	Primitive per-node state; read as the initial condition and overwritten with the advanced one

Returns: Sub-cycle count, CFL bound and the positivity minima

Exceptions

std::invalid_argument	if the array lengths disagree, thermo is null, or the boundary is not subsonic outflow where OuterBc::PressureOutlet assumes it
std::runtime_error	if a sub-cycle leaves a node with a non-positive density, a non-positive electron density while an electron species is present, or non-finite

Definition at line 138 of file HydroStep.cpp.

◆ loadMechanism()

std::shared_ptr< Cantera::Solution > rizer::loadMechanism	(	const std::string &	mech,
		const std::string &	phase )

Load a mechanism with rizer's custom rate types registered first.

The registration has to happen before the YAML is parsed, or a mechanism naming one of those rates fails to load. Every model in this extension needs the same two calls in the same order, so they live here rather than once per model.

Parameters

[in]	mech	Cantera mechanism (YAML) path
[in]	phase	Phase name within mech

Returns: The loaded Solution

Definition at line 88 of file PlasmaRates.cpp.

◆ monatomicElectronCv()

double rizer::monatomicElectronCv ( double electron_molecular_weight )

inline

Electron specific heat at constant volume, per kg of ELECTRONS, \(c_{v,\mathrm{e}}=\tfrac32 R/W_\mathrm{e}\).

Analytic, not a thermo fit: a free electron gas is monatomic whatever the heavy pool is made of, which is what lets NUMERICS.md section 8 invert the electron temperature in closed form.

This is the closed form itself. ThermoAccessor::electronCv() is the interface a caller holding a state reaches for, and every implementation of it ends up here; the two carry different names so that a call inside one of those implementations means what it reads as.

Parameters

[in] electron_molecular_weight \(W_\mathrm{e}\) [kg/kmol]

Returns: Electron \(c_v\) [J/kg of electrons/K]

Definition at line 64 of file PlasmaState.h.

◆ parseOuterBc()

OuterBc rizer::parseOuterBc ( const std::string & mode )

Map an outer_bc_mode config string onto the enum.

Lives beside the enum rather than in a caller so that whoever takes the config string can reject an unknown one before any work is done, rather than at the first sub-step that happens to need it.

Parameters

mode	Config value, "ambient_ghost" or "pressure_outlet"

Exceptions

std::invalid_argument on any other value

Definition at line 13 of file BoundaryConditions.cpp.

◆ readTwoTemperatureState()

TwoTemperatureState rizer::readTwoTemperatureState ( const Cantera::PlasmaPhase & phase )

inline

Read the two-temperature EOS back from a phase whose state is set.

Parameters

[in] phase Phase to read; its state is not modified

Returns: The quantities above, at that state

Definition at line 84 of file PlasmaState.h.

◆ registerPlasmaRates()

void rizer::registerPlasmaRates ( )

Register the custom plasma reaction rates with Cantera's ReactionRateFactory.

Idempotent (factory reg replaces silently); safe to call before every newSolution. Call this before loading any mechanism that uses janev-dissociative-recombination-C2Hy, Druyvesteyn, or reverse-two-temperature-plasma.

Definition at line 95 of file PlasmaRates.cpp.

◆ significant()

std::string rizer::significant ( double value )

inline

value to 6 significant digits, for exception messages.

std::to_string prints six fixed decimals, which turns a nanosecond time or a sub-mm radius into 0.000000.

Parameters

[in] value Number to format

Returns: Its text

Definition at line 18 of file Format.h.

◆ solveChannelTransient()

ChannelHistory rizer::solveChannelTransient ( const ChannelOptions & opts )

Build a PlasmaChannel1D from opts.cfg, advance it from t=0 to \(t = \mathtt{opts.dt} \cdot \mathtt{opts.n\_steps}\) [s] with the stiff BDF backend, and return the recorded radial history.

Throws Cantera::CanteraError if the integrator fails to converge (see solveChannelTransient's own comments for how a CVODE failure is decoded before being re-raised).

Parameters

opts	Mechanism/grid/transport config, dt/n_steps/record_every/ and loglevel

Applied field E(t) [V/m]: the circuit's when one is closed, the prescribed constant or schedule otherwise.

Appends the circuit columns for the frame record has just appended.

< Start in the global state [-]

< Components owned [-]

The one node this system owns, or Cantera::npos when it owns the whole domain. Only the error decoder needs it: a single-node system reports component indices relative to itself, so there is no node number in them to recover.

Definition at line 480 of file PlasmaChannelSolver.cpp.

◆ solveColumn()

ColumnResult rizer::solveColumn	(	double	R,
		double	electric_field,
		double	T_wall,
		const PropertyTable &	sigma,
		const PropertyTable &	kappa,
		const PropertyTable &	p_rad,
		const ColumnOptions &	opts )

Build, solve, and extract the radial Elenbaas-Heller column.

Parameters

R	Outer wall radius [m]
electric_field	Axial E field [V/m], held fixed for this solve
T_wall	Wall (boundary) temperature [K] at r=R
sigma	Electrical conductivity table \(\sigma(T)\) [S/m] vs. T [K]
kappa	Thermal conductivity table \(\kappa(T)\) [W/m/K] vs. T [K]
p_rad	Volumetric radiative loss table \(P_\text{rad}(T)\) [W/m^3] vs. T [K]
opts	Solver configuration (grid, refinement, initial guess, etc.)

Exceptions

std::invalid_argument	if only one of opts.init_r / opts.init_T is given, or they differ in length, or have fewer than 2 points.
std::runtime_error	if the converged temperature is outside the sigma, kappa or p_rad table.

Definition at line 22 of file PlasmaColumnSolver.cpp.

◆ throwOutsideTable()

void rizer::throwOutsideTable	(	const PropertyTable &	table,
		double	x,
		const char *	procedure,
		const std::string &	what,
		const char *	unit,
		const char *	remedy )

inline

Throw the TrialStateError for x outside table.

Parameters

[in]	table	Table that does not cover `x`, not empty
[in]	x	State variable it was asked for [units of the abscissa]
[in]	procedure	Function evaluating it, for the exception
[in]	what	Name of the tabulated property, for the exception
[in]	unit	Unit of the abscissa, for the exception
[in]	remedy	What the caller can change to cover the state

Exceptions

TrialStateError always

Definition at line 30 of file TableLookup.h.

◆ wallEnergyOutflow()

WallEnergyOutflow rizer::wallEnergyOutflow	(	const PlasmaChannel1D &	domain,
		Cantera::span< const double >	x,
		const RadialDiffusionCoefficients &	c,
		const double *	species_enthalpy )

What conduction and species diffusion move through the wall face at the state x.

The parabolic terms are flux differences, so summed over every cell their interior faces cancel and the wall face is all that is left: this is the term an energy budget over the domain has to carry for them, the way it carries boundary_total_energy_out for the hydro sub-step.

The diffusion term charges each species' face mass flux at species_enthalpy, which is what the Fickian and compressibility terms deposit in the outermost cell between them. The enthalpy-diffusion term is a product of centred gradients, not a face flux, so it has no wall term here; its departure from conservation is a second-order interior remainder, not a boundary flux.

Parameters

[in]	domain	Grid and state layout
[in]	x	This domain's state vector
[in]	c	Coefficients and ghosts, as addRadialDiffusion()
[in]	species_enthalpy	Mass-basis enthalpy of each species at the outermost node [J/kg], length K; see PlasmaCell::speciesEnthalpies

Returns: The two energy outflows [W/m] and the species mass outflow

Definition at line 273 of file RadialDiffusion.cpp.

Variable Documentation

◆ Boltzmann

double rizer::Boltzmann = units::k_b

constexpr

Definition at line 49 of file PlasmaState.h.

◆ ElectronGamma

double rizer::ElectronGamma = 5.0 / 3.0

constexpr

Ratio of specific heats of the electron pool [-].

Analytic, not a thermo fit: a free electron gas is monatomic, so \(\gamma_\mathrm{e}=5/3\) whatever the heavy pool is made of. The frozen sound speed of PHYSICS.md appendix A.4 needs it separately from the heavy pool's gamma because the electron enters the pressure at \(X_\mathrm{e}\) while it enters a mass-weighted gamma at \(Y_\mathrm{e}\), four orders smaller.

Definition at line 22 of file ThermoAccessor.h.

◆ GasConstant

double rizer::GasConstant = units::R_kmol

constexpr

Universal gas constant [J/kmol/K] and Boltzmann's constant [J/K], from units.h rather than Cantera's CODATA-2018 values, to match the Python reactor reference this extension is a port of.

Definition at line 48 of file PlasmaState.h.

◆ TemperatureCeiling

double rizer::TemperatureCeiling = 1.0e5

constexpr

Upper limit of the physically meaningful range [K].

Above it the NASA polynomials are extrapolating and a state is far likelier to be a diverged iterate than a real one: the hottest measured point in this repo is the P4 case's 22.5 kK electron temperature (NUMERICS.md section "Validation ladder"), so this leaves a factor of four. The extrapolation is not benign: the CH4 mechanism's C+, C++ and C+++ fits give cp/R < 1, a negative c_v, from 1.52e5 K.

Definition at line 43 of file PlasmaState.h.

◆ TemperatureFloor

double rizer::TemperatureFloor = 200.0

constexpr

Lower limit of the mechanism's NASA polynomials [K].

Cantera has no meaningful thermo below it and an integrator can undershoot into it.

Definition at line 34 of file PlasmaState.h.

Namespaces

Classes

Typedefs

Enumerations

Functions

Variables

Typedef Documentation

◆ GhostStateFn

Enumeration Type Documentation

◆ OuterBc

Function Documentation

◆ addRadialDiffusion()

◆ buildElectronReactionIndex()

◆ equationHasElectron()

◆ evalAtState()

◆ hydroStep()

◆ loadMechanism()

◆ monatomicElectronCv()

◆ parseOuterBc()

◆ readTwoTemperatureState()

◆ registerPlasmaRates()

◆ significant()

◆ solveChannelTransient()

◆ solveColumn()

◆ throwOutsideTable()

◆ wallEnergyOutflow()

Variable Documentation

◆ Boltzmann

◆ ElectronGamma

◆ GasConstant

◆ TemperatureCeiling

◆ TemperatureFloor