TimeStepper for evaluating the streamer inception criterion in static or transient electric fields. More...

#include <CD_DischargeInceptionStepper.H>

Inheritance diagram for Physics::DischargeInception::DischargeInceptionStepper< P, F, C >:

Collaboration diagram for Physics::DischargeInception::DischargeInceptionStepper< P, F, C >:

Public Member Functions
	DischargeInceptionStepper ()
	Default constructor.

	DischargeInceptionStepper (const DischargeInceptionStepper &)=delete
	Disallowed constructor.

	DischargeInceptionStepper (const DischargeInceptionStepper &&)=delete
	Disallowed constructor.

virtual	~DischargeInceptionStepper ()
	Destructor.

DischargeInceptionStepper &	operator= (const DischargeInceptionStepper &)=delete
	Disallowed assignment.

DischargeInceptionStepper &	operator= (const DischargeInceptionStepper &&)=delete
	Disallowed assignment.

void	setupSolvers () override
	Instantiate the tracer particle solver.

void	allocate () override
	Allocate storage for solvers and time stepper.

void	initialData () override
	Fill problem with initial data.

void	postInitialize () override
	Perform any post-initialization steps.

void	postCheckpointSetup () override
	Post checkpoint operations.

void	registerRealms () override
	Register realms. Primal is the only realm we need.

void	registerOperators () override
	Register operators.

void	parseOptions ()
	Parse options.

void	parseRuntimeOptions () override
	Parse runtime options.

virtual int	getNumberOfPlotVariables () const override
	Get the number of plot variables for this time stepper.

virtual Vector< std::string >	getPlotVariableNames () const override
	Get plot variable names.

virtual void	writePlotData (LevelData< EBCellFAB > &a_output, int &a_icomp, const std::string &a_outputRealm, const int a_level) const override
	Write plot data to output holder.

virtual Vector< std::string >	getStationaryPlotVariableNames () const noexcept
	Get plot variable names for stationary mode.

virtual Vector< std::string >	getTransientPlotVariableNames () const noexcept
	Get plot variable names for transient mode.

virtual Real	computeDt () override
	Compute a time step to be used by Driver.

virtual Real	advance (const Real a_dt) override
	Advancement method. Swaps between various kernels.

virtual void	advanceIons (const Real a_dt) noexcept
	Advance negative ions.

virtual void	synchronizeSolverTimes (const int a_step, const Real a_time, const Real a_dt) override
	Synchronize solver times and time steps.

virtual void	printStepReport () override
	Print a step report. Used in transient simulations.

virtual void	preRegrid (const int a_lmin, const int a_oldFinestLevel) override
	Perform pre-regrid operations.

virtual void	regrid (const int a_lmin, const int a_oldFinestLevel, const int a_newFinestLevel) override
	Time stepper regrid method.

virtual void	postRegrid () override
	Perform post-regrid operations.

virtual void	setVoltageCurve (const std::function< Real(const Real &a_time)> &a_voltageCurve) noexcept
	Set the voltage curve (used for transient mode)

virtual void	setRho (const std::function< Real(const RealVect &x)> &a_rho) noexcept
	Set space charge distribution.

virtual void	setSigma (const std::function< Real(const RealVect &x)> &a_sigma) noexcept
	Set surface charge distribution.

virtual void	setIonDensity (const std::function< Real(const RealVect x)> &a_density) noexcept
	Set the negative ion density.

virtual void	setIonMobility (const std::function< Real(const Real E)> &a_mobility) noexcept
	Set the negative ion mobility (field-dependent)

virtual void	setIonDiffusion (const std::function< Real(const Real E)> &a_diffCo) noexcept
	Set the negative ion diffusion coefficient (field-dependent)

virtual void	setAlpha (const std::function< Real(const Real &E, const RealVect &x)> &a_alpha) noexcept
	Set the ionization coefficient.

virtual void	setEta (const std::function< Real(const Real &E, const RealVect &x)> &a_eta) noexcept
	Set the attachment coefficient.

virtual const std::function< Real(const Real &E, const RealVect &x)> &	getAlpha () const noexcept
	Get ionization coefficient.

virtual const std::function< Real(const Real &E, const RealVect &x)> &	getEta () const noexcept
	Get attachment coefficient.

virtual void	setBackgroundRate (const std::function< Real(const Real &E, const RealVect &x)> &a_backgroundRate) noexcept
	Set the background ionization rate (e.g. from cosmic radiation etc).

virtual void	setDetachmentRate (const std::function< Real(const Real &E, const RealVect &x)> &a_detachmentRate) noexcept
	Set the detachment rate for negative ions.

virtual void	setFieldEmission (const std::function< Real(const Real &E, const RealVect &x)> &a_currentDensity) noexcept
	Set the field emission current.

virtual void	setSecondaryEmission (const std::function< Real(const Real &E, const RealVect &x)> &a_coeff) noexcept
	Set the secondary emission coefficient.

virtual Mode	getMode () const noexcept
	Get the solver mode.

virtual const EBAMRCellData *	getElectricField () const noexcept
	Get the electric field.

Public Member Functions inherited from TimeStepper
	TimeStepper ()
	Default constructor (does nothing)

virtual	~TimeStepper ()
	Default destructor (does nothing)

	TimeStepper (const TimeStepper &)=delete
	Disallow copy construction.

TimeStepper &	operator= (const TimeStepper &)=delete
	Disallow copy assignment.

	TimeStepper (TimeStepper &&)=default
	Allow move construction.

TimeStepper &	operator= (TimeStepper &&)=default
	Allow move assignment.

void	setAmr (const RefCountedPtr< AmrMesh > &a_amr)
	Set AmrMesh.

void	setComputationalGeometry (const RefCountedPtr< ComputationalGeometry > &a_computationalGeometry)
	Set the computational geometry.

virtual void	prePlot ()
	An option for calling special functions prior to plotting data. Called by Driver in the IMMEDIATELY before writing the plot file.

virtual void	postPlot ()
	An option for calling special functions prior to plotting data. Called by Driver in the IMMEDIATELY after writing the plot file.

virtual Vector< long int >	getCheckpointLoads (const std::string &a_realm, int a_level) const
	Get computational loads to be checkpointed.

virtual bool	needToRegrid ()
	Function which can have Driver do regrids at arbitrary points in the simulation.

bool	keepGoing () const
	Query whether the time stepper wants to continue stepping.

virtual bool	loadBalanceThisRealm (const std::string &a_realm) const
	Load balancing query for a specified realm. If this returns true for a_realm, load balancing routines will be called during regrids.

virtual void	loadBalanceBoxes (Vector< Vector< int > > &a_procs, Vector< Vector< Box > > &a_boxes, const std::string &a_realm, const Vector< DisjointBoxLayout > &a_grids, int a_lmin, int a_finestLevel)
	Load balance grid boxes for a specified realm.

Protected Member Functions
virtual void	seedUniformParticles () noexcept
	Distribute particles in every grid cell.

virtual void	seedIonizationParticles (const Real a_voltage) noexcept
	Add particles to every cell where alpha - eta > 0.0.

virtual void	computeInceptionIntegral (EBAMRCellData &a_inceptionIntegral, const Real a_voltage) noexcept
	Compute the inception integral for the input voltage.

virtual void	computeInceptionIntegralStationary () noexcept
	Solve streamer inception integral for each particle in each voltage and store K values in m_inceptionIntegral.

virtual void	computeInceptionIntegralTransient (const Real &a_voltage) noexcept
	Solve streamer inception integral.

virtual void	inceptionIntegrateEuler (const Real &a_voltage) noexcept
	Integrate the inception integral using the Euler rule.

virtual void	inceptionIntegrateTrapezoidal (const Real &a_voltage) noexcept
	K integral: Add integration parts after particles move.

virtual void	interpolateGradAlphaToParticles () noexcept
	Interpolate alpha/\|grad(alpha)\| onto some scratch particle storage.

virtual void	computeTownsendCriterionStationary () noexcept
	Solve for the Townsend criterion for each particle in each voltage.

virtual void	computeTownsendCriterionTransient (const Real &a_voltage) noexcept
	Solve for the Townsend criterion for each particle in each voltage.

virtual void	townsendTrackEuler (const Real &a_voltage) noexcept
	Track particles (positive ions) using an Euler rule and check if the collide with a cathode.

virtual void	townsendTrackTrapezoidal (const Real &a_voltage) noexcept
	Track particles (positive ions) using a trapezoidal rule and check if the collide with a cathode.

virtual Real	computeRdot (const Real &a_voltage) const noexcept
	Compute integral_Vcr(done/dt * (1 - eta/alpha) dV)

virtual void	rewindTracerParticles () noexcept
	Move particles back to their original position.

virtual void	resetTracerParticles () noexcept
	Reset particles.

virtual void	computeBackgroundIonizationStationary () noexcept
	Compute the background ionization rate for all voltages.

virtual void	computeDetachmentStationary () noexcept
	Compute the detachment ionization rate for all voltages.

virtual void	computeFieldEmissionStationary () noexcept
	Compute field emission rates.

virtual void	computeFieldEmission (EBAMRCellData &a_emissionRate, const Real &a_voltage) const noexcept
	Compute field emission rates.

virtual void	evaluateFunction (EBAMRCellData &a_data, const Real &a_voltage, const std::function< Real(const Real E, const RealVect x)> &a_func) const noexcept
	Evaluate a function f = f(E, x) in a volume.

virtual void	evaluateFunction (LevelData< EBCellFAB > &a_data, const Real &a_voltage, const std::function< Real(const Real E, const RealVect x)> &a_func, const int a_level) const noexcept
	Evaluate a function f = f(E,x) in a volume.

virtual void	computeInceptionVoltageVolume () noexcept
	Interpolate between K values to find voltage giving K_inception and store values in m_inceptionVoltage.

virtual std::pair< Real, RealVect >	computeMinimumInceptionVoltage (const EBAMRCellData &a_Uinc) const noexcept
	Compute the minimum inception voltage and the starting electron position.

virtual void	computeCriticalVolumeStationary () noexcept
	Compute the critical volume of the K values for each voltage.

virtual Real	computeCriticalVolumeTransient () const noexcept
	Compute the critical volume of the K values for each voltage.

virtual void	computeCriticalAreaStationary () noexcept
	Compute the critical area of the K values for each voltage.

virtual Real	computeCriticalAreaTransient () const noexcept
	Compute the critical area of the K values for each voltage.

virtual void	computeIonizationVolumeStationary () noexcept
	Compute the ionization volume for each voltage.

virtual Real	computeIonizationVolumeTransient (const Real &a_voltage) const noexcept
	Compute the ionization volume for each voltage.

virtual void	writeReportStationary () const noexcept
	Print report to the terminal.

virtual void	writeReportTransient () const noexcept
	Print report to the terminal.

virtual void	writePlotDataStationary (LevelData< EBCellFAB > &a_output, int &a_icomp, const std::string &a_outputRealm, const int a_level) const noexcept
	Write plot data for the 'stationary' mode.

virtual void	writePlotDataTransient (LevelData< EBCellFAB > &a_output, int &a_icomp, const std::string &a_outputRealm, const int a_level) const noexcept
	Write plot data for the 'transient' mode.

bool	particleOutsideGrid (const RealVect &a_pos, const RealVect &a_probLo, const RealVect &a_probHi) const noexcept
	Check if particle is outside grid boundaries.

bool	particleInsideEB (const RealVect &a_pos) const noexcept
	Check if particle is inside electrode.

void	computeIonVelocity (const Real &a_voltage) noexcept
	Set the negative ion velocity. Note.

void	computeIonDiffusion (const Real &a_voltage) noexcept
	Set the negative ion diffusion coefficient.

void	parseMode () noexcept
	Parse simulation mode.

void	parseVoltages () noexcept
	Parse voltage levels.

void	parseOutput () noexcept
	Parse output settings.

void	parseVerbosity () noexcept
	Parse class verbosity.

void	parseInceptionAlgorithm () noexcept
	Parse the inception algorithm.

void	parseTransportAlgorithm () noexcept
	Parse the transport algorithm.

void	parsePlotVariables () noexcept
	Parse plot variables.

void	solvePoisson () noexcept
	Solve the Poisson equation.

void	superposition (EBAMRCellData &a_sumField, const MFAMRCellData &a_inhomogeneousField, const MFAMRCellData &a_homogeneousField, const Real a_voltage) const noexcept
	Calculate the total electric field = inhomogeneous + V * homogeneous.

void	superposition (EBAMRCellData &a_sumField, const Real a_voltage) const noexcept
	Update the input field with the scaled voltage.

virtual void	writeData (LevelData< EBCellFAB > &a_output, int &a_comp, const EBAMRCellData &a_data, const std::string a_outputRealm, const int a_level, const bool a_interpToCentroids, const bool a_interpGhost) const noexcept
	Write data to output. Convenience function used for IO.

virtual void	getMaxValueAndLocation (Real &a_maxVal, RealVect &a_maxPos, const EBAMRCellData &a_data) const noexcept
	Get the maximum value and location corresponding to the maximum value in the input data holder.

virtual Real	getCriticalField () const noexcept
	Get the breakdown field.

Protected Attributes
Mode	m_mode
	Mode.

IntegrationAlgorithm	m_inceptionAlgorithm
	Integration algorithm for K-value.

TransportAlgorithm	m_transportAlgorithm
	Transport algorithm for advancing negative ions in the transient mode.

TimeStepRestriction	m_timeStepRestriction
	Time step restriction.

RefCountedPtr< TracerParticleSolver< P > >	m_tracerParticleSolver
	Tracer particle solver.

RefCountedPtr< FieldSolver >	m_fieldSolver
	Field solver.

RefCountedPtr< CdrSolver >	m_ionSolver
	Negative ion solver.

MFAMRCellData	m_potential
	Electric potential.

MFAMRCellData	m_potentialHomo
	Electric potential without charges.

MFAMRCellData	m_potentialInho
	Electric potential with charges.

MFAMRCellData	m_scratchHomo
	Scratch storage used during regrids.

MFAMRCellData	m_scratchInho
	Scratch storage used during regrids.

MFAMRCellData	m_electricField
	Electric field.

MFAMRCellData	m_electricFieldHomo
	Electric field without space/surface charge and V = 1 on live electrodes.

MFAMRCellData	m_electricFieldInho
	Electric field with space/surface charge and V = 0 on all electrodes.

EBAMRCellData	m_homogeneousFieldGas
	Gas-phase homogeneous field.

EBAMRCellData	m_inceptionIntegral
	Inception integral values.

Vector< EBAMRCellData >	m_inceptionIntegralPlus
	Inception integral values.

Vector< EBAMRCellData >	m_inceptionIntegralMinu
	Inception integral values.

Vector< EBAMRCellData >	m_backgroundIonizationStationary
	Background ionization rates.

Vector< EBAMRCellData >	m_detachmentStationary
	Detachment rates.

Vector< EBAMRCellData >	m_emissionRatesPlus
	Field emission rates.

Vector< EBAMRCellData >	m_emissionRatesMinu
	Field emission rates.

Vector< EBAMRCellData >	m_townsendCriterionPlus
	Townsend criterion for starting positive ions.

Vector< EBAMRCellData >	m_townsendCriterionMinu
	Townsend criterion for starting negative ions (electrons arriving at anode).

EBAMRCellData	m_emissionRate
	Field emission rates.

EBAMRCellData	m_inceptionVoltagePlus
	Computed inception voltage.

EBAMRCellData	m_inceptionVoltageMinu
	Computed inception voltage.

EBAMRCellData	m_streamerInceptionVoltagePlus
	Computed streamer inception voltage.

EBAMRCellData	m_streamerInceptionVoltageMinu
	Computed streamer inception voltage.

EBAMRCellData	m_townsendInceptionVoltagePlus
	Computed Townsend inception voltage.

EBAMRCellData	m_townsendInceptionVoltageMinu
	Computed Townsend inception voltage.

EBAMRCellData	m_townsendCriterion
	Townsend criterion.

EBAMRCellData	m_detachment
	Detachment factor.

EBAMRCellData	m_backgroundIonization
	Background ionization.

EBAMRCellData	m_gradAlpha
	Calculated version of alpha/(\|grad(alpha)\|) on the mesh.

std::vector< std::tuple< Real, Real, RealVect > >	m_KPlusValues
	Max K value for every voltage.

std::vector< std::tuple< Real, Real, RealVect > >	m_KMinuValues
	Max K value for every voltage.

std::vector< std::tuple< Real, Real, RealVect > >	m_TPlusValues
	Max T value for every voltage.

std::vector< std::tuple< Real, Real, RealVect > >	m_TMinuValues
	Max T value for every voltage.

std::vector< std::pair< Real, Real > >	m_maxK
	Max K value for every time step.

std::vector< std::pair< Real, Real > >	m_maxT
	Max Townsend value for every time step.

std::vector< Real >	m_criticalVolumePlus
	Critical volumes of K values for each voltage.

std::vector< Real >	m_criticalVolumeMinu
	Critical volumes of K values for each voltage.

std::vector< Real >	m_criticalAreaPlus
	Critical area of K values for each voltage.

std::vector< Real >	m_criticalAreaMinu
	Critical area of K values for each voltage.

std::vector< Real >	m_ionizationVolume
	Ionization volumes for each voltage.

std::vector< Real >	m_RdotPlus
	Rate of appearance of first electron (in critical volume)

std::vector< Real >	m_RdotMinu
	Rate of appearance of first electron (in critical volume)

std::vector< Real >	m_voltageSweeps
	Voltage sweeps.

std::vector< std::pair< Real, Real > >	m_Rdot
	Integral factor for cumulative integration.

std::vector< std::pair< Real, Real > >	m_inceptionProbability
	Cumulative probability of breakdown by time t.

std::vector< std::pair< Real, Real > >	m_criticalVolume
	Critical volume at various time instances.

std::vector< std::pair< Real, Real > >	m_criticalArea
	Critical area at various time instances.

std::vector< std::pair< Real, Real > >	m_ionizationVolumeTransient
	Ionization volume at various time instances.

Real	m_relativeDeltaU
	Maximum relative voltage increase.

Real	m_deltaK
	Maximum targeted increase in K-value.

Real	m_maxKLimit
	Maximum K-value that is calculated in stationary mode.

Real	m_cfl
	CFL-step for negative ions.

Real	m_firstDt
	First time step.

Real	m_maxDt
	Maximum permitted time step.

Real	m_minDt
	Minimum permitted time step.

Real	m_epsVoltage
	Permitted relative deviation in V(t) when computing voltage-curve based time steps.

Real	m_maxDtGrowth
	Maximum permitted time step growth.

Real	m_minPhysDx
	Minimum spatial step (physical dimensions)

Real	m_maxPhysDx
	Maximum spatial step (physical dimensions)

Real	m_minGridDx
	Minimum spatial step (relative to grid resolution)

Real	m_maxGridDx
	Maximum spatial step (relative to grid resolution)

Real	m_alphaDx
	Space step size relative to 1/alpha.

Real	m_townsendGridDx
	Space step size used for ion tracking.

Real	m_gradAlphaDx
	Space step size relative to alpha/\|grad(alpha)\|.

Real	m_inceptionK
	Inception criteria (read from input)

bool	m_profile
	Profile calculation or not.

bool	m_debug
	Debug or not.

bool	m_evaluateTownsend
	Evaluate secondary emission.

bool	m_fullIntegration
	Use full reconstruction of critical volume or not.

bool	m_ionTransport
	Ion transport on/off.

bool	m_plotField
	Plot field.

bool	m_plotPoisson
	Plot Poisson solver or not.

bool	m_plotTracer
	Plot tracer particle solver or not.

bool	m_plotNegativeIons
	Plot negative ions or not.

bool	m_plotInceptionIntegral
	If true, plot the K-values.

bool	m_plotInceptionVoltage
	If true, plot the inception voltage.

bool	m_plotBackgroundIonization
	If true, plot the background ionization rates.

bool	m_plotDetachment
	If true, plot electron detachment rate, i.e. done/dt due to detachment from negative ions.

bool	m_plotFieldEmission
	If true, plot the field emission.

bool	m_plotAlpha
	If true, plot alpha.

bool	m_plotEta
	If true, plot eta.

bool	m_plotTownsend
	Plot the Townsend-criterion for initiatory ions.

std::function< Real(const Real a_time)>	m_voltageCurve
	Time-dependent voltage.

std::string	m_realm
	Realm where the solver lives.

std::string	m_dataOutputFile
	File name for the tabular data output (inception voltages, K-values, etc.).

std::string	m_outputFile
	File name prefix for HDF5 plot output.

phase::which_phase	m_phase
	Phase (gas/solid) where the solver lives.

std::function< Real(const RealVect &x)>	m_rho
	Space charge distribution.

std::function< Real(const RealVect &x)>	m_sigma
	Surface charge distribution.

std::function< Real(const RealVect &x)>	m_initialIonDensity
	Negative ion density.

std::function< Real(const Real &E)>	m_ionMobility
	Negative ion mobility.

std::function< Real(const Real &E)>	m_ionDiffusion
	Negative ion diffusion coefficient.

std::function< Real(const Real &E, const RealVect &x)>	m_alpha
	Ionization coefficient.

std::function< Real(const Real &E, const RealVect &x)>	m_eta
	Attachment coefficient.

std::function< Real(const Real &E, const RealVect &x)>	m_detachmentRate
	Detachment probability for negative ion.

std::function< Real(const Real &E, const RealVect &x)>	m_backgroundRate
	Background ionization rate expression.

std::function< Real(const Real &E, const RealVect &x)>	m_fieldEmission
	Field emission current.

std::function< Real(const Real &E, const RealVect &x)>	m_secondaryEmission
	Secondary emission coefficient.

Protected Attributes inherited from TimeStepper
int	m_verbosity
	Class verbosity.

int	m_timeStep
	Time step.

Real	m_time
	TIme.

Real	m_dt
	Previous time step size.

bool	m_keepGoing
	If false, Driver will stop the time loop after the current step.

RefCountedPtr< AmrMesh >	m_amr
	AmrMesh.

RefCountedPtr< ComputationalGeometry >	m_computationalGeometry
	Computational geometry.

Detailed Description

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>
class Physics::DischargeInception::DischargeInceptionStepper< P, F, C >

TimeStepper for evaluating the streamer inception criterion in static or transient electric fields.

This class solves for the streamer inception voltage (stationary mode) or the time-dependent inception probability (transient mode) by tracing the paths of seed electrons through the electric field and integrating the effective ionization coefficient along those paths.

The class is templated on three solver types:

P: Tracer particle type (default TracerParticle<2,3>). Each particle carries the inception integral K and additional per-particle state.
F: Field solver type (default FieldSolverGMG). Solves the Poisson equation for the electric potential, decomposed into homogeneous (V=1 on live electrodes, no charges) and inhomogeneous (V=0 on all electrodes, space/surface charges) contributions that are superimposed at run time.
C: CDR solver type (default CdrCTU). Advances the negative ion density in transient mode.

In stationary mode the class sweeps over a user-supplied voltage range, computes the inception integral K for each seed position and voltage, and derives the inception voltage map and the critical volume/area. In transient mode the voltage follows a user-supplied curve and the inception probability is accumulated over time together with ion transport.

Member Function Documentation

◆ advance()

template<typename P , typename F , typename C >

Real DischargeInceptionStepper::advance ( const Real a_dt )

overridevirtual

Advancement method. Swaps between various kernels.

Parameters

[in] a_dt Time step to be used for advancement

Returns: Returns the time step that was used (equal to a_dt in this case).

Implements TimeStepper.

◆ advanceIons()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::advanceIons ( const Real a_dt )

virtualnoexcept

Advance negative ions.

Parameters

[in] a_dt Description

◆ allocate()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::allocate ( )

overridevirtual

Allocate storage for solvers and time stepper.

Implements TimeStepper.

◆ computeBackgroundIonizationStationary()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::computeBackgroundIonizationStationary ( )

protectedvirtualnoexcept

Compute the background ionization rate for all voltages.

Note: For stationary simulations.

◆ computeCriticalAreaStationary()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::computeCriticalAreaStationary ( )

protectedvirtualnoexcept

Compute the critical area of the K values for each voltage.

Note: For the stationary method

◆ computeCriticalAreaTransient()

template<typename P , typename F , typename C >

Real DischargeInceptionStepper::computeCriticalAreaTransient ( ) const

protectedvirtualnoexcept

Compute the critical area of the K values for each voltage.

Note: For the transient method

Returns: Computed critical area transient

◆ computeCriticalVolumeStationary()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::computeCriticalVolumeStationary ( )

protectedvirtualnoexcept

Compute the critical volume of the K values for each voltage.

Note: For the stationary method

◆ computeCriticalVolumeTransient()

template<typename P , typename F , typename C >

Real DischargeInceptionStepper::computeCriticalVolumeTransient ( ) const

protectedvirtualnoexcept

Compute the critical volume of the K values for each voltage.

Note: Transient approach.

Returns: Computed critical volume transient

◆ computeDetachmentStationary()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::computeDetachmentStationary ( )

protectedvirtualnoexcept

Compute the detachment ionization rate for all voltages.

Note: For stationary simulations.

◆ computeDt()

template<typename P , typename F , typename C >

Real DischargeInceptionStepper::computeDt ( )

overridevirtual

Compute a time step to be used by Driver.

Returns: Computed dt

Implements TimeStepper.

◆ computeFieldEmission()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::computeFieldEmission	(	EBAMRCellData &	a_emissionRate,
		const Real &	a_voltage
	)		const

protectedvirtualnoexcept

Compute field emission rates.

Parameters

[out]	a_emissionRate	Field emission rate.
[in]	a_voltage	Voltage multiplier

Note: For plotting the emission rate in transient simulations.

◆ computeFieldEmissionStationary()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::computeFieldEmissionStationary ( )

protectedvirtualnoexcept

Compute field emission rates.

Note: For stationary simulations.

◆ computeInceptionIntegral()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::computeInceptionIntegral	(	EBAMRCellData &	a_inceptionIntegral,
		const Real	a_voltage
	)

protectedvirtualnoexcept

Compute the inception integral for the input voltage.

Parameters

[out]	a_inceptionIntegral	Mesh storage for the inception integral
[in]	a_voltage	Applied voltage (can be positive or negative).

◆ computeInceptionIntegralStationary()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::computeInceptionIntegralStationary ( )

protectedvirtualnoexcept

Solve streamer inception integral for each particle in each voltage and store K values in m_inceptionIntegral.

This is called in postInitialize() only.

Note: For stationary mode only.

◆ computeInceptionIntegralTransient()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::computeInceptionIntegralTransient ( const Real & a_voltage )

protectedvirtualnoexcept

Solve streamer inception integral.

Called in postInitialize and the advance method

Note: Transient mode only.

Parameters

[in] a_voltage Voltage multiplier

◆ computeInceptionVoltageVolume()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::computeInceptionVoltageVolume ( )

protectedvirtualnoexcept

Interpolate between K values to find voltage giving K_inception and store values in m_inceptionVoltage.

This is the volumetric version.

◆ computeIonDiffusion()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::computeIonDiffusion ( const Real & a_voltage )

inlineprotectednoexcept

Set the negative ion diffusion coefficient.

Parameters

[in] a_voltage Current voltage

◆ computeIonizationVolumeStationary()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::computeIonizationVolumeStationary ( )

protectedvirtualnoexcept

Compute the ionization volume for each voltage.

Note: For the stationary method

◆ computeIonizationVolumeTransient()

template<typename P , typename F , typename C >

Real DischargeInceptionStepper::computeIonizationVolumeTransient ( const Real & a_voltage ) const

protectedvirtualnoexcept

Compute the ionization volume for each voltage.

Note: For the transient method

Returns: Computed ionization volume transient

Parameters

[in,out] a_voltage Description

◆ computeIonVelocity()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::computeIonVelocity ( const Real & a_voltage )

inlineprotectednoexcept

Set the negative ion velocity. Note.

Parameters

[in] a_voltage Current voltage

◆ computeMinimumInceptionVoltage()

template<typename P , typename F , typename C >

std::pair< Real, RealVect > DischargeInceptionStepper::computeMinimumInceptionVoltage ( const EBAMRCellData & a_Uinc ) const

protectedvirtualnoexcept

Compute the minimum inception voltage and the starting electron position.

Parameters

[in] a_Uinc Inception voltage for all starting positions.

Returns: Computed minimum inception voltage

◆ computeRdot()

template<typename P , typename F , typename C >

Real DischargeInceptionStepper::computeRdot ( const Real & a_voltage ) const

protectedvirtualnoexcept

Compute integral_Vcr(done/dt * (1 - eta/alpha) dV)

Parameters

[in] a_voltage Voltage multiplier.

Returns: Computed rdot

◆ computeTownsendCriterionStationary()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::computeTownsendCriterionStationary ( )

protectedvirtualnoexcept

Solve for the Townsend criterion for each particle in each voltage.

This is called in postInitialize() only.

Note: For stationary mode only.

◆ computeTownsendCriterionTransient()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::computeTownsendCriterionTransient ( const Real & a_voltage )

protectedvirtualnoexcept

Solve for the Townsend criterion for each particle in each voltage.

Parameters

[in] a_voltage Voltage multiplier

Note: For transient mode

◆ evaluateFunction() [1/2]

template<typename P , typename F , typename C >

void DischargeInceptionStepper::evaluateFunction	(	EBAMRCellData &	a_data,
		const Real &	a_voltage,
		const std::function< Real(const Real E, const RealVect x)> &	a_func
	)		const

protectedvirtualnoexcept

Evaluate a function f = f(E, x) in a volume.

Parameters

[out]	a_data	Mesh data
[in]	a_voltage	Voltage multiplier
[in]	a_func	Function to evaluate

Note: For plotting the emission rate in transient simulations.

◆ evaluateFunction() [2/2]

template<typename P , typename F , typename C >

void DischargeInceptionStepper::evaluateFunction	(	LevelData< EBCellFAB > &	a_data,
		const Real &	a_voltage,
		const std::function< Real(const Real E, const RealVect x)> &	a_func,
		const int	a_level
	)		const

protectedvirtualnoexcept

Evaluate a function f = f(E,x) in a volume.

Parameters

[out]	a_data	Mesh data
[in]	a_voltage	Voltage multiplier
[in]	a_func	Function to evaluate
[in]	a_level	Grid level

Note: For plotting the emission rate in transient simulations.

◆ getAlpha()

template<typename P , typename F , typename C >

const std::function< Real(const Real &E, const RealVect &x)> & DischargeInceptionStepper::getAlpha ( ) const

virtualnoexcept

Get ionization coefficient.

Returns: Alpha

◆ getCriticalField()

template<typename P , typename F , typename C >

Real DischargeInceptionStepper::getCriticalField ( ) const

protectedvirtualnoexcept

Get the breakdown field.

Returns: Critical field

◆ getElectricField()

template<typename P , typename F , typename C >

const EBAMRCellData * DischargeInceptionStepper::getElectricField ( ) const

virtualnoexcept

Get the electric field.

Returns: Electric field

◆ getEta()

template<typename P , typename F , typename C >

const std::function< Real(const Real &E, const RealVect &x)> & DischargeInceptionStepper::getEta ( ) const

virtualnoexcept

Get attachment coefficient.

Returns: Eta

◆ getMaxValueAndLocation()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::getMaxValueAndLocation	(	Real &	a_maxVal,
		RealVect &	a_maxPos,
		const EBAMRCellData &	a_data
	)		const

protectedvirtualnoexcept

Get the maximum value and location corresponding to the maximum value in the input data holder.

Parameters

[out]	a_maxVal	Maximum value.
[out]	a_maxPos	Position where maximum value was found
[in]	a_data	Mesh data

◆ getMode()

template<typename P , typename F , typename C >

Mode DischargeInceptionStepper::getMode ( ) const

virtualnoexcept

Get the solver mode.

Returns: Mode

◆ getNumberOfPlotVariables()

template<typename P , typename F , typename C >

int DischargeInceptionStepper::getNumberOfPlotVariables ( ) const

overridevirtual

Get the number of plot variables for this time stepper.

This is necessary because Driver, not TimeStepper, is responsible for allocating the necessary memory.

Returns: Returns number of plot variables that will be written during writePlotData

Implements TimeStepper.

◆ getPlotVariableNames()

template<typename P , typename F , typename C >

Vector< std::string > DischargeInceptionStepper::getPlotVariableNames ( ) const

overridevirtual

Get plot variable names.

Returns: Plot variable names

Implements TimeStepper.

◆ getStationaryPlotVariableNames()

template<typename P , typename F , typename C >

Vector< std::string > DischargeInceptionStepper::getStationaryPlotVariableNames ( ) const

virtualnoexcept

Get plot variable names for stationary mode.

Returns: Stationary plot variable names

◆ getTransientPlotVariableNames()

template<typename P , typename F , typename C >

Vector< std::string > DischargeInceptionStepper::getTransientPlotVariableNames ( ) const

virtualnoexcept

Get plot variable names for transient mode.

Returns: Transient plot variable names

◆ inceptionIntegrateEuler()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::inceptionIntegrateEuler ( const Real & a_voltage )

protectedvirtualnoexcept

Integrate the inception integral using the Euler rule.

Parameters

[in,out] a_voltage Description

◆ inceptionIntegrateTrapezoidal()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::inceptionIntegrateTrapezoidal ( const Real & a_voltage )

protectedvirtualnoexcept

K integral: Add integration parts after particles move.

Parameters

[in] a_voltage Voltage multiplier

◆ initialData()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::initialData ( )

overridevirtual

Fill problem with initial data.

Implements TimeStepper.

◆ parseRuntimeOptions()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::parseRuntimeOptions ( )

overridevirtual

Parse runtime options.

Reimplemented from TimeStepper.

◆ particleInsideEB()

template<typename P , typename F , typename C >

bool DischargeInceptionStepper::particleInsideEB ( const RealVect & a_pos ) const

inlineprotectednoexcept

Check if particle is inside electrode.

Parameters

[in] a_pos Particle position

Returns: true if particle inside electrode, false elsewise

◆ particleOutsideGrid()

template<typename P , typename F , typename C >

bool DischargeInceptionStepper::particleOutsideGrid	(	const RealVect &	a_pos,
		const RealVect &	a_probLo,
		const RealVect &	a_probHi
	)		const

inlineprotectednoexcept

Check if particle is outside grid boundaries.

Parameters

[in]	a_pos	Particle position
[in]	a_probLo	Lower left boundary of grid
[in]	a_probHi	Upper right boundary of grid

Returns: true if particle outside boundary, false elsewise

◆ postCheckpointSetup()

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

void Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::postCheckpointSetup ( )

inlineoverridevirtual

Post checkpoint operations.

Note: Not needed for this time stepper because checkpoint-restart is not supported.

Implements TimeStepper.

◆ postInitialize()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::postInitialize ( )

overridevirtual

Perform any post-initialization steps.

Implements TimeStepper.

◆ postRegrid()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::postRegrid ( )

overridevirtual

Perform post-regrid operations.

This includes all operations to be done AFTER interpolating data to new grids.

Implements TimeStepper.

◆ preRegrid()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::preRegrid	(	const int	a_lmin,
		const int	a_oldFinestLevel
	)

overridevirtual

Perform pre-regrid operations.

Parameters

[in]	a_lmin	The coarsest level that changes
[in]	a_oldFinestLevel	The finest level before the regrid.

Implements TimeStepper.

◆ printStepReport()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::printStepReport ( )

overridevirtual

Print a step report. Used in transient simulations.

Implements TimeStepper.

◆ registerOperators()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::registerOperators ( )

overridevirtual

Register operators.

Only need the solver's operators.

Implements TimeStepper.

◆ registerRealms()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::registerRealms ( )

overridevirtual

Register realms. Primal is the only realm we need.

Implements TimeStepper.

◆ regrid()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::regrid	(	const int	a_lmin,
		const int	a_oldFinestLevel,
		const int	a_newFinestLevel
	)

overridevirtual

Time stepper regrid method.

Parameters

[in]	a_lmin	The coarsest level that changed.
[in]	a_oldFinestLevel	The finest level before the regrid.
[in]	a_newFinestLevel	The finest level after the regrid.

Implements TimeStepper.

◆ seedIonizationParticles()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::seedIonizationParticles ( const Real a_voltage )

protectedvirtualnoexcept

Add particles to every cell where alpha - eta > 0.0.

This also populates the alpha/grad(alpha) container.

Parameters

[in] a_voltage Input voltage

◆ setAlpha()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::setAlpha ( const std::function< Real(const Real &E, const RealVect &x)> & a_alpha )

virtualnoexcept

Set the ionization coefficient.

Parameters

[in] a_alpha Townsend ionization coefficient. E is the field in SI units.

◆ setBackgroundRate()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::setBackgroundRate ( const std::function< Real(const Real &E, const RealVect &x)> & a_backgroundRate )

virtualnoexcept

Set the background ionization rate (e.g. from cosmic radiation etc).

Parameters

[in] a_backgroundRate Background ionization rate (units of 1/m^3 s).

◆ setDetachmentRate()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::setDetachmentRate ( const std::function< Real(const Real &E, const RealVect &x)> & a_detachmentRate )

virtualnoexcept

Set the detachment rate for negative ions.

The total detachment rate is dn_e/dt = k*n_ion; this sets the constant k.

Parameters

[in] a_detachmentRate Detachment rate (in units of 1/s).

◆ setEta()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::setEta ( const std::function< Real(const Real &E, const RealVect &x)> & a_eta )

virtualnoexcept

Set the attachment coefficient.

Parameters

[in] a_eta Townsend attachment coefficient. E is the field in SI units.

◆ setFieldEmission()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::setFieldEmission ( const std::function< Real(const Real &E, const RealVect &x)> & a_currentDensity )

virtualnoexcept

Set the field emission current.

Parameters

[in] a_currentDensity Current density

◆ setIonDensity()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::setIonDensity ( const std::function< Real(const RealVect x)> & a_density )

virtualnoexcept

Set the negative ion density.

Parameters

[in] a_density Negative ion density

◆ setIonDiffusion()

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

void DischargeInceptionStepper::setIonDiffusion ( const std::function< Real(const Real E)> & a_diffCo )

virtualnoexcept

Set the negative ion diffusion coefficient (field-dependent)

Parameters

[in] a_diffCo Negative ion diffusion coefficient

◆ setIonMobility()

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

void DischargeInceptionStepper::setIonMobility ( const std::function< Real(const Real E)> & a_mobility )

virtualnoexcept

Set the negative ion mobility (field-dependent)

Parameters

[in] a_mobility Negative ion mobility

◆ setRho()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::setRho ( const std::function< Real(const RealVect &x)> & a_rho )

virtualnoexcept

Set space charge distribution.

Parameters

[in] a_rho Space charge distribution

◆ setSecondaryEmission()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::setSecondaryEmission ( const std::function< Real(const Real &E, const RealVect &x)> & a_coeff )

virtualnoexcept

Set the secondary emission coefficient.

Parameters

[in] a_coeff Secondary emission coefficient.

◆ setSigma()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::setSigma ( const std::function< Real(const RealVect &x)> & a_sigma )

virtualnoexcept

Set surface charge distribution.

Parameters

[in] a_sigma Surface charge distribution

◆ setupSolvers()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::setupSolvers ( )

overridevirtual

Instantiate the tracer particle solver.

Implements TimeStepper.

◆ setVoltageCurve()

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

void DischargeInceptionStepper::setVoltageCurve ( const std::function< Real(const Real &a_time)> & a_voltageCurve )

virtualnoexcept

Set the voltage curve (used for transient mode)

Parameters

[in] a_voltageCurve Voltage curve

◆ superposition() [1/2]

template<typename P , typename F , typename C >

void DischargeInceptionStepper::superposition	(	EBAMRCellData &	a_sumField,
		const MFAMRCellData &	a_inhomogeneousField,
		const MFAMRCellData &	a_homogeneousField,
		const Real	a_voltage
	)		const

inlineprotectednoexcept

Calculate the total electric field = inhomogeneous + V * homogeneous.

Parameters

[in]	a_sumField	Sum of contributions
[in]	a_inhomogeneousField	Inhomogeneous field contribution
[in]	a_voltage	Electrode voltage
[in]	a_homogeneousField	Homogeneous field

◆ superposition() [2/2]

template<typename P , typename F , typename C >

void DischargeInceptionStepper::superposition	(	EBAMRCellData &	a_sumField,
		const Real	a_voltage
	)		const

inlineprotectednoexcept

Update the input field with the scaled voltage.

Parameters

[out]	a_sumField	Sum of fields
[in]	a_voltage	Electrode voltage

◆ synchronizeSolverTimes()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::synchronizeSolverTimes	(	const int	a_step,
		const Real	a_time,
		const Real	a_dt
	)

overridevirtual

Synchronize solver times and time steps.

Parameters

[in]	a_step	Time step
[in]	a_time	Time (in seconds)
[in]	a_dt	Time step that was used.

Implements TimeStepper.

◆ townsendTrackEuler()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::townsendTrackEuler ( const Real & a_voltage )

protectedvirtualnoexcept

Track particles (positive ions) using an Euler rule and check if the collide with a cathode.

Parameters

[in] a_voltage Voltage multiplier

◆ townsendTrackTrapezoidal()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::townsendTrackTrapezoidal ( const Real & a_voltage )

protectedvirtualnoexcept

Track particles (positive ions) using a trapezoidal rule and check if the collide with a cathode.

Parameters

[in] a_voltage Voltage multiplier

◆ writeData()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::writeData	(	LevelData< EBCellFAB > &	a_output,
		int &	a_comp,
		const EBAMRCellData &	a_data,
		const std::string	a_outputRealm,
		const int	a_level,
		const bool	a_interpToCentroids,
		const bool	a_interpGhost
	)		const

protectedvirtualnoexcept

Write data to output. Convenience function used for IO.

Parameters

[in,out]	a_output	Output data holder.
[in]	a_data	Data to write.
[in]	a_outputRealm	Realm where a_output belongs
[in]	a_level	Grid level
[in]	a_interpToCentroids	If true, a_data will be interpolated to cell centroids before writing to a_output.
[in]	a_interpGhost	If true, interpolate ghost cells
[in]	a_comp	Comp

◆ writePlotData()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::writePlotData	(	LevelData< EBCellFAB > &	a_output,
		int &	a_icomp,
		const std::string &	a_outputRealm,
		const int	a_level
	)		const

overridevirtual

Write plot data to output holder.

Parameters

[in,out]	a_output	Output data holder.
[in,out]	a_icomp	Starting component in a_output to begin at.
[in]	a_outputRealm	Realm where a_output belongs
[in]	a_level	Grid level

Implements TimeStepper.

◆ writePlotDataStationary()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::writePlotDataStationary	(	LevelData< EBCellFAB > &	a_output,
		int &	a_icomp,
		const std::string &	a_outputRealm,
		const int	a_level
	)		const

protectedvirtualnoexcept

Write plot data for the 'stationary' mode.

Parameters

[in,out]	a_output	Output data holder.
[in,out]	a_icomp	Starting component in a_output to begin at.
[in]	a_outputRealm	Realm where a_output belongs
[in]	a_level	Grid level

◆ writePlotDataTransient()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::writePlotDataTransient	(	LevelData< EBCellFAB > &	a_output,
		int &	a_icomp,
		const std::string &	a_outputRealm,
		const int	a_level
	)		const

protectedvirtualnoexcept

Write plot data for the 'transient' mode.

Parameters

[in,out]	a_output	Output data holder.
[in]	a_outputRealm	Realm where a_output belongs
[in,out]	a_icomp	Starting component in a_output to begin at.
[in]	a_level	Level

◆ writeReportStationary()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::writeReportStationary ( ) const

protectedvirtualnoexcept

Print report to the terminal.

Note: For stationary runs

◆ writeReportTransient()

template<typename P , typename F , typename C >

void DischargeInceptionStepper::writeReportTransient ( ) const

protectedvirtualnoexcept

Print report to the terminal.

Note: For transient runs. Called in the constructor.

Member Data Documentation

◆ m_backgroundIonization

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

EBAMRCellData Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::m_backgroundIonization

protected

Background ionization.

Note: Transient mode.

◆ m_backgroundIonizationStationary

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

Vector<EBAMRCellData> Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::m_backgroundIonizationStationary

protected

Background ionization rates.

Note: Both modes.

◆ m_criticalArea

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

std::vector<std::pair<Real, Real> > Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::m_criticalArea

protected

Critical area at various time instances.

First parameter is time, second parameter is the critical area.

◆ m_criticalAreaMinu

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

std::vector<Real> Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::m_criticalAreaMinu

protected

Critical area of K values for each voltage.

Note: Stationary mode, negative polarity

◆ m_criticalAreaPlus

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

std::vector<Real> Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::m_criticalAreaPlus

protected

Critical area of K values for each voltage.

Note: Stationary mode, positive polarity

◆ m_criticalVolume

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

std::vector<std::pair<Real, Real> > Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::m_criticalVolume

protected

Critical volume at various time instances.

First parameter is time, second parameter is the critical volume.

◆ m_criticalVolumeMinu

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

std::vector<Real> Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::m_criticalVolumeMinu

protected

Critical volumes of K values for each voltage.

Note: Stationary mode, negative polarity

◆ m_criticalVolumePlus

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

std::vector<Real> Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::m_criticalVolumePlus

protected

Critical volumes of K values for each voltage.

Note: Stationary mode, positive polarity

◆ m_deltaK

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

Real Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::m_deltaK

protected

Maximum targeted increase in K-value.

Only for stationary mode.

◆ m_detachment

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

EBAMRCellData Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::m_detachment

protected

Detachment factor.

Note: Transient mode.

◆ m_detachmentStationary

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

Vector<EBAMRCellData> Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::m_detachmentStationary

protected

Detachment rates.

Note: Both modes.

◆ m_emissionRate

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

EBAMRCellData Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::m_emissionRate

protected

Field emission rates.

Note: Used for transient mode.

◆ m_emissionRatesMinu

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

Vector<EBAMRCellData> Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::m_emissionRatesMinu

protected

Field emission rates.

Note: Stationary mode, negative polarity

◆ m_emissionRatesPlus

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

Vector<EBAMRCellData> Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::m_emissionRatesPlus

protected

Field emission rates.

Note: Stationary mode, positive polarity

◆ m_inceptionIntegral

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

EBAMRCellData Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::m_inceptionIntegral

protected

Inception integral values.

Note: Transient mode.

◆ m_inceptionIntegralMinu

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

Vector<EBAMRCellData> Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::m_inceptionIntegralMinu

protected

Inception integral values.

Note: Stationary mode, negative polarity

◆ m_inceptionIntegralPlus

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

Vector<EBAMRCellData> Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::m_inceptionIntegralPlus

protected

Inception integral values.

Note: Stationary mode, positive polarity

◆ m_inceptionProbability

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

std::vector<std::pair<Real, Real> > Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::m_inceptionProbability

protected

Cumulative probability of breakdown by time t.

First parameter is time, second parameter is breakdown probability.

◆ m_inceptionVoltageMinu

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

EBAMRCellData Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::m_inceptionVoltageMinu

protected

Computed inception voltage.

Note: Stationary mode, negative polarity

◆ m_inceptionVoltagePlus

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

EBAMRCellData Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::m_inceptionVoltagePlus

protected

Computed inception voltage.

Note: Stationary mode, positive polarity

◆ m_ionizationVolume

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

std::vector<Real> Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::m_ionizationVolume

protected

Ionization volumes for each voltage.

Note: Stationary mode

◆ m_ionizationVolumeTransient

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

std::vector<std::pair<Real, Real> > Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::m_ionizationVolumeTransient

protected

Ionization volume at various time instances.

First parameter is time, second parameter is the ionization volume.

◆ m_KMinuValues

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

std::vector<std::tuple<Real, Real, RealVect> > Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::m_KMinuValues

protected

Max K value for every voltage.

Note: Stationary mode and negative polarity. The tuple contains (|voltage|, K-value, max position)

◆ m_KPlusValues

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

std::vector<std::tuple<Real, Real, RealVect> > Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::m_KPlusValues

protected

Max K value for every voltage.

Note: Stationary mode and positive polarity. The tuple contains (|voltage|, K-value, max position)

◆ m_maxK

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

std::vector<std::pair<Real, Real> > Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::m_maxK

protected

Max K value for every time step.

Note: For transient runs

◆ m_maxT

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

std::vector<std::pair<Real, Real> > Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::m_maxT

protected

Max Townsend value for every time step.

Note: For transient runs

◆ m_Rdot

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

std::vector<std::pair<Real, Real> > Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::m_Rdot

protected

Integral factor for cumulative integration.

This is the integral_Vcr done/dt * (1 - eta/alpha) dV + integral(j/e*dS) stored at each time step.

Note: Only for transient mode.

◆ m_RdotMinu

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

std::vector<Real> Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::m_RdotMinu

protected

Rate of appearance of first electron (in critical volume)

Note: Stationary mode, negative polarity.

◆ m_RdotPlus

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

std::vector<Real> Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::m_RdotPlus

protected

Rate of appearance of first electron (in critical volume)

Note: Stationary mode, positive polarity.

◆ m_relativeDeltaU

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

Real Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::m_relativeDeltaU

protected

Maximum relative voltage increase.

Only for stationary mode.

◆ m_streamerInceptionVoltageMinu

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

EBAMRCellData Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::m_streamerInceptionVoltageMinu

protected

Computed streamer inception voltage.

Note: Stationary mode, negative polarity

◆ m_streamerInceptionVoltagePlus

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

EBAMRCellData Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::m_streamerInceptionVoltagePlus

protected

Computed streamer inception voltage.

Note: Stationary mode, positive polarity

◆ m_TMinuValues

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

std::vector<std::tuple<Real, Real, RealVect> > Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::m_TMinuValues

protected

Max T value for every voltage.

Note: Stationary mode and negative polarity. The tuple contains (|voltage|, K-value, max position)

◆ m_townsendCriterion

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

EBAMRCellData Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::m_townsendCriterion

protected

Townsend criterion.

Note: Transient mode.

◆ m_townsendCriterionMinu

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

Vector<EBAMRCellData> Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::m_townsendCriterionMinu

protected

Townsend criterion for starting negative ions (electrons arriving at anode).

Note: Stationary mode.

◆ m_townsendCriterionPlus

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

Vector<EBAMRCellData> Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::m_townsendCriterionPlus

protected

Townsend criterion for starting positive ions.

Note: Stationary mode

◆ m_townsendInceptionVoltageMinu

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

EBAMRCellData Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::m_townsendInceptionVoltageMinu

protected

Computed Townsend inception voltage.

Note: Stationary mode, negative polarity

◆ m_townsendInceptionVoltagePlus

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

EBAMRCellData Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::m_townsendInceptionVoltagePlus

protected

Computed Townsend inception voltage.

Note: Stationary mode, positive polarity

◆ m_TPlusValues

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

std::vector<std::tuple<Real, Real, RealVect> > Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::m_TPlusValues

protected

Max T value for every voltage.

Note: Stationary mode and positive polarity. The tuple contains (|voltage|, K-value, max position)

◆ m_voltageSweeps

template<typename P = TracerParticle<2, 3>, typename F = FieldSolverGMG, typename C = CdrCTU>

std::vector<Real> Physics::DischargeInception::DischargeInceptionStepper< P, F, C >::m_voltageSweeps

protected

Voltage sweeps.

Note: Stationary mode

The documentation for this class was generated from the following files:

Physics/DischargeInception/CD_DischargeInceptionStepper.H
Physics/DischargeInception/CD_DischargeInceptionStepperImplem.H

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Member Function Documentation

◆ advance()

◆ advanceIons()

◆ allocate()

◆ computeBackgroundIonizationStationary()

◆ computeCriticalAreaStationary()

◆ computeCriticalAreaTransient()

◆ computeCriticalVolumeStationary()

◆ computeCriticalVolumeTransient()

◆ computeDetachmentStationary()

◆ computeDt()

◆ computeFieldEmission()

◆ computeFieldEmissionStationary()

◆ computeInceptionIntegral()

◆ computeInceptionIntegralStationary()

◆ computeInceptionIntegralTransient()

◆ computeInceptionVoltageVolume()

◆ computeIonDiffusion()

◆ computeIonizationVolumeStationary()

◆ computeIonizationVolumeTransient()

◆ computeIonVelocity()

◆ computeMinimumInceptionVoltage()

◆ computeRdot()

◆ computeTownsendCriterionStationary()

◆ computeTownsendCriterionTransient()

◆ evaluateFunction() [1/2]

◆ evaluateFunction() [2/2]

◆ getAlpha()

◆ getCriticalField()

◆ getElectricField()

◆ getEta()

◆ getMaxValueAndLocation()

◆ getMode()

◆ getNumberOfPlotVariables()

◆ getPlotVariableNames()

◆ getStationaryPlotVariableNames()

◆ getTransientPlotVariableNames()

◆ inceptionIntegrateEuler()

◆ inceptionIntegrateTrapezoidal()

◆ initialData()

◆ parseRuntimeOptions()

◆ particleInsideEB()

◆ particleOutsideGrid()

◆ postCheckpointSetup()

◆ postInitialize()

◆ postRegrid()

◆ preRegrid()

◆ printStepReport()

◆ registerOperators()

◆ registerRealms()

◆ regrid()

◆ seedIonizationParticles()

◆ setAlpha()

◆ setBackgroundRate()

◆ setDetachmentRate()

◆ setEta()

◆ setFieldEmission()

◆ setIonDensity()

◆ setIonDiffusion()

◆ setIonMobility()

◆ setRho()

◆ setSecondaryEmission()

◆ setSigma()

◆ setupSolvers()

◆ setVoltageCurve()

◆ superposition() [1/2]

◆ superposition() [2/2]

◆ synchronizeSolverTimes()

◆ townsendTrackEuler()

◆ townsendTrackTrapezoidal()

◆ writeData()

◆ writePlotData()

◆ writePlotDataStationary()

◆ writePlotDataTransient()

◆ writeReportStationary()

◆ writeReportTransient()