mtnlion.models.isothermal module¶

Base Newman isothermal model

class mtnlion.models.isothermal.Isothermal(num_functions)[source]¶

Bases: mtnlion.model.Model

The basic DFN lithium-ion model with no thermal considerations and a 1D approximation of the solid concentration.

class ElectrolyteConcentration[source]¶

Bases: mtnlion.formula.Formula

Concentration of lithium in the electrolyte.

form(arguments, domain)[source]¶

This method must be overloaded to define the form of the Formula.

Parameters

arguments – All arguments defined by overriding one or more of Formula.Variables, Formula.Formulas, Formula.Parameters, Formula.Lambdas, and Formula.TimeDiscretization
domain – The current domain in which the function is being evaluated

Returns

FFL form

class ElectrolytePotential[source]¶

Bases: mtnlion.formula.Formula

Charge conservation in the electrolyte.

form(arguments, domain)[source]¶

This method must be overloaded to define the form of the Formula.

Parameters

arguments – All arguments defined by overriding one or more of Formula.Variables, Formula.Formulas, Formula.Parameters, Formula.Lambdas, and Formula.TimeDiscretization
domain – The current domain in which the function is being evaluated

Returns

FFL form

class ExchangeCurrentDensity[source]¶

Bases: mtnlion.formula.Formula

The exchange current density is the current in the absence of net electrolysis and at zero overpotential.

form(arguments, domain)[source]¶

This method must be overloaded to define the form of the Formula.

Parameters

arguments – All arguments defined by overriding one or more of Formula.Variables, Formula.Formulas, Formula.Parameters, Formula.Lambdas, and Formula.TimeDiscretization
domain – The current domain in which the function is being evaluated

Returns

FFL form

class IntercalationFlux[source]¶

Bases: mtnlion.formula.Formula

Describes how the electrical current on an electrode depends on the electrode potential.

form(arguments, domain)[source]¶

This method must be overloaded to define the form of the Formula.

Parameters

arguments – All arguments defined by overriding one or more of Formula.Variables, Formula.Formulas, Formula.Parameters, Formula.Lambdas, and Formula.TimeDiscretization
domain – The current domain in which the function is being evaluated

Returns

FFL form

class KappaDEff[source]¶

Bases: mtnlion.formula.Formula

kappa_d effective

form(arguments, domain)[source]¶

This method must be overloaded to define the form of the Formula.

Parameters

arguments – All arguments defined by overriding one or more of Formula.Variables, Formula.Formulas, Formula.Parameters, Formula.Lambdas, and Formula.TimeDiscretization
domain – The current domain in which the function is being evaluated

Returns

FFL form

class KappaEff[source]¶

Bases: mtnlion.formula.Formula

Effective conductivity of the electrolyte.

form(arguments, domain)[source]¶

This method must be overloaded to define the form of the Formula.

Parameters

arguments – All arguments defined by overriding one or more of Formula.Variables, Formula.Formulas, Formula.Parameters, Formula.Lambdas, and Formula.TimeDiscretization
domain – The current domain in which the function is being evaluated

Returns

FFL form

class KappaRef[source]¶

Bases: mtnlion.formula.Formula

Bulk conductivity of the homogeneous materials.

form(arguments, domain)[source]¶

This method must be overloaded to define the form of the Formula.

Parameters

arguments – All arguments defined by overriding one or more of Formula.Variables, Formula.Formulas, Formula.Parameters, Formula.Lambdas, and Formula.TimeDiscretization
domain – The current domain in which the function is being evaluated

Returns

FFL form

class OpenCircuitPotential[source]¶

Bases: mtnlion.formula.Formula

Open-circuit potential formula.

form(arguments, domain)[source]¶: Evaluate the open-circuit potential equation.

class Overpotential[source]¶

Bases: mtnlion.formula.Formula

Voltage difference between a reduction potential and the potential of the redox event.

form(arguments, domain)[source]¶

This method must be overloaded to define the form of the Formula.

Parameters

arguments – All arguments defined by overriding one or more of Formula.Variables, Formula.Formulas, Formula.Parameters, Formula.Lambdas, and Formula.TimeDiscretization
domain – The current domain in which the function is being evaluated

Returns

FFL form

class SolidConcentration(legendre)[source]¶

Bases: mtnlion.formula.Formula

Concentration of lithium in the solid, 1D approximation using Legendre polynomials.

form(arguments, domain)[source]¶

This method must be overloaded to define the form of the Formula.

Parameters

arguments – All arguments defined by overriding one or more of Formula.Variables, Formula.Formulas, Formula.Parameters, Formula.Lambdas, and Formula.TimeDiscretization
domain – The current domain in which the function is being evaluated

Returns

FFL form

class SolidConcentrationBoundary[source]¶

Bases: mtnlion.formula.Formula

This Formula defines the value of the lithium concentration at the surface of the solid particle.

form(arguments, domain)[source]¶

This method must be overloaded to define the form of the Formula.

Parameters

arguments – All arguments defined by overriding one or more of Formula.Variables, Formula.Formulas, Formula.Parameters, Formula.Lambdas, and Formula.TimeDiscretization
domain – The current domain in which the function is being evaluated

Returns

FFL form

class SolidConcentrationNeumann[source]¶

Bases: mtnlion.formula.Formula

Nuemann boundary for the solid concentration. This Formula doesn’t use a boundary domain due to the 1D 1D approximation.

form(arguments, domain)[source]¶

This method must be overloaded to define the form of the Formula.

Parameters

arguments – All arguments defined by overriding one or more of Formula.Variables, Formula.Formulas, Formula.Parameters, Formula.Lambdas, and Formula.TimeDiscretization
domain – The current domain in which the function is being evaluated

Returns

FFL form

class SolidPotential[source]¶

Bases: mtnlion.formula.Formula

Charge conservation in the solid.

form(arguments, domain)[source]¶

This method must be overloaded to define the form of the Formula.

Parameters

arguments – All arguments defined by overriding one or more of Formula.Variables, Formula.Formulas, Formula.Parameters, Formula.Lambdas, and Formula.TimeDiscretization
domain – The current domain in which the function is being evaluated

Returns

FFL form

class SolidPotentialNeumann[source]¶

Bases: mtnlion.formula.Formula

Neumann boundary for the solid potential at the anode/cathode current collector boundaries.

form(arguments, domain)[source]¶

This method must be overloaded to define the form of the Formula.

Parameters

arguments – All arguments defined by overriding one or more of Formula.Variables, Formula.Formulas, Formula.Parameters, Formula.Lambdas, and Formula.TimeDiscretization
domain – The current domain in which the function is being evaluated

Returns

FFL form

class StateOfCharge[source]¶

Bases: mtnlion.formula.Formula

State of Charge (SOC) formula.

form(arguments, domain)[source]¶

This method must be overloaded to define the form of the Formula.

Parameters

arguments – All arguments defined by overriding one or more of Formula.Variables, Formula.Formulas, Formula.Parameters, Formula.Lambdas, and Formula.TimeDiscretization
domain – The current domain in which the function is being evaluated

Returns

FFL form