mtnlion.formulas.dfn module

A collection of formulas useful for the Doyl-Fuller-Newman cell model

class mtnlion.formulas.dfn.CapacityLoss

Bases: mtnlion.formula.Formula

Capacity loss due to the side reactions.

form(arguments, domain)

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 mtnlion.formulas.dfn.FilmResistance

Bases: mtnlion.formula.Formula

Resistance of the film that builds around the surface of the particles.

form(arguments, domain)

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 mtnlion.formulas.dfn.FilmThickness

Bases: mtnlion.formula.Formula

Thickness of the film that builds around the surface of the particles.

form(arguments, domain)

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 mtnlion.formulas.dfn.KappaDEff

Bases: mtnlion.formula.Formula

kappa_d effective

form(arguments, domain)

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 mtnlion.formulas.dfn.KappaEff

Bases: mtnlion.formula.Formula

Effective conductivity of the electrolyte.

form(arguments, domain)

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 mtnlion.formulas.dfn.KappaRef(kappa_ref_str)

Bases: mtnlion.formula.Formula

Bulk conductivity of the homogeneous materials.

form(arguments, domain)

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 mtnlion.formulas.dfn.SOC

Bases: mtnlion.formula.Formula

State of Charge (SOC) formula.

form(arguments, domain)

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 mtnlion.formulas.dfn.Uocp(uocp_str)

Bases: mtnlion.formula.Formula

Open-circuit potential formula.

form(arguments, domain)

Evaluate the open-circuit potential equation.

mtnlion.formulas.dfn.eval_form(formula: mtnlion.formula.Formula, *parameters) → mtnlion.domain.Domain[str, ufl.core.expr.Expr]

Evaluate a formula with the provided parameters. Note: The order of the parameters must match the definition of the formula.

Parameters

• formula – Formula to evaluate

• parameters – Parameters to use for evaluation

Returns

FFL expression