X-averaged Polynomial Profile

class pybamm.particle.no_distribution.XAveragedPolynomialProfile(param, domain, name)

Class for molar conservation in a single x-averaged particle with an assumed polynomial concentration profile in r. Model equations from 1.

Parameters

• param (parameter class) – The parameters to use for this submodel

• domain (str) – The domain of the model either ‘Negative’ or ‘Positive’

• name (str) – The name of the polynomial approximation to be used. Can be “uniform profile”, “quadratic profile” or “quartic profile”.

References

1

VR Subramanian, VD Diwakar and D Tapriyal. “Efficient Macro-Micro Scale Coupled Modeling of Batteries”. Journal of The Electrochemical Society, 152(10):A2002-A2008, 2005

Extends: pybamm.particle.BaseParticle

get_coupled_variables(variables)

A public method that creates and returns the variables in a submodel which require variables in other submodels to be set first. For example, the exchange current density requires the concentration in the electrolyte to be created before it can be created. If a variable can be created independent of other submodels then it should be created in ‘get_fundamental_variables’ instead of this method.

Parameters

variables (dict) – The variables in the whole model.

Returns

The variables created in this submodel which depend on variables in other submodels.

Return type

dict

get_fundamental_variables()

A public method that creates and returns the variables in a submodel which can be created independent of other submodels. For example, the electrolyte concentration variables can be created independent of whether any other variables have been defined in the model. As a rule, if a variable can be created without variables from other submodels, then it should be placed in this method.

Returns

The variables created by the submodel which are independent of variables in other submodels.

Return type

dict

set_initial_conditions(variables)

For single or x-averaged particle models, initial conditions can’t depend on x so we arbitrarily evaluate them at x=0 in the negative electrode and x=1 in the positive electrode (they will usually be constant)

set_rhs(variables)

A method to set the right hand side of the differential equations which contain a time derivative. Note: this method modifies the state of self.rhs. Unless overwritten by a submodel, the default behaviour of ‘pass’ is used as implemented in pybamm.BaseSubModel.

Parameters

variables (dict) – The variables in the whole model.