bmlite.SPM.dae#

The dae module provides the system of differential algebraic equations (DAE) for the SPM model. In addition, the bandwidth function is included in this module, which helps determine the lower and upper bandwidths of residuals so the 'band' linear solver option can be used in the IDASolver class.

Functions#

residuals(t, sv, svdot, res, inputs)

The DAE residuals res = M*y' - f(t, y) for the SPM model.

sign(x)

Return +1 for x >= 0, -1 for x < 0.

Module Contents#

bmlite.SPM.dae.residuals(t, sv, svdot, res, inputs)[source]#

The DAE residuals res = M*y' - f(t, y) for the SPM model.

Parameters:

  • t (float) – Value of time [s].

  • sv (1D array) – Solution/state variables at time t.

  • svdot (1D array) – Solution/state variable time derivatives at time t.

  • res (1D array) – An array the same size as sv and svdot. The values are filled in with res = M*y' - f(t, y) inside this function.

  • inputs ((sim : SPM Simulation object, exp : experiment dict)) – The simulation object and experimental details dictionary inputs that describe the specific battery and experiment to simulate.

Returns:

outputs (tuple[np.ndarray]) – If the experimental step mode is set to post, then the following post-processed variables will be returned in a tuple. Otherwise, returns None.

Variable

Description [units] (type)

sdot_an

anode Li+ production [kmol/m3/s] (1D array)

sdot_ca

cathode Li+ production [kmol/m3/s] (1D array)

bmlite.SPM.dae.sign(x)[source]#

Return +1 for x >= 0, -1 for x < 0.