This example requires external dependencies and cannot be run in the browser.

High-Fidelity DFN Simulation via Co-Simulation

The Doyle–Fuller–Newman (DFN) model produces a DAE system after discretisation and cannot be used with the monolithic ODE blocks. The co-simulation blocks (CellCoSimElectrothermal, CellCoSimElectrical) let PyBaMM step the DAE internally while PathSim receives zero-order-held outputs between macro-steps.

Why Co-Simulation?

The DFN model resolves spatial gradients in both the solid and electrolyte phases. The phase-potential equations are algebraic, so after spatial discretisation the DFN becomes a DAE — incompatible with CellElectrical / CellElectrothermal.

The co-simulation blocks call pybamm.Simulation.step() internally on a fixed macro-step dt and expose zero-order-held outputs to PathSim. This supports any PyBaMM model.

Brosa Planella et al., arXiv:2203.16091 (2022).

Python

/opt/hostedtoolcache/Python/3.11.16/x64/lib/python3.11/site-packages/tqdm/auto.py:21: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html
  from .autonotebook import tqdm as notebook_tqdm

Part 1: SPMe vs DFN with Built-in Thermal

Both models use PyBaMM's lumped thermal sub-model. SPMe runs as a monolithic ODE in PathSim; DFN runs via co-simulation with a 10 s macro-step.

Python

Running SPMe (monolithic)...
12:03:34 - INFO - LOGGING (log: True)
12:03:34 - INFO - BLOCKS (total: 4, dynamic: 1, static: 3, eventful: 0)
12:03:34 - INFO - GRAPH (nodes: 4, edges: 5, alg. depth: 2, loop depth: 0, runtime: 0.056ms)
12:03:34 - INFO - STARTING -> TRANSIENT (Duration: 1800.00s)
12:03:34 - INFO - --------------------   1% | 0.1s<9.3s | 19.8 it/s
12:03:34 - INFO - ####----------------  20% | 0.4s<1.2s | 19.3 it/s
12:03:34 - INFO - ###########---------  56% | 0.6s<0.3s | 15.9 it/s
12:03:34 - INFO - #################---  88% | 0.7s<0.1s | 14.7 it/s
12:03:35 - INFO - #################### 100% | 0.8s<--:-- | 14.1 it/s
12:03:35 - INFO - FINISHED -> TRANSIENT (total steps: 13, successful: 13, runtime: 770.48 ms)

Python

Running DFN (co-simulation)...
12:03:35 - INFO - LOGGING (log: True)
12:03:35 - INFO - BLOCKS (total: 4, dynamic: 0, static: 4, eventful: 1)
12:03:35 - INFO - GRAPH (nodes: 4, edges: 5, alg. depth: 2, loop depth: 0, runtime: 0.045ms)
12:03:35 - INFO - STARTING -> TRANSIENT (Duration: 1800.00s)
12:03:36 - INFO - --------------------   1% | 0.7s<30.2s | 5.9 it/s
12:03:37 - INFO - ##------------------  10% | 1.7s<10.2s | 15.8 it/s
12:03:38 - INFO - ###-----------------  18% | 2.8s<9.6s | 15.3 it/s
12:03:38 - INFO - ####----------------  20% | 3.0s<9.4s | 15.4 it/s
12:03:39 - INFO - ######--------------  31% | 4.0s<4.7s | 26.1 it/s
12:03:40 - INFO - ########------------  40% | 4.6s<4.4s | 24.5 it/s
12:03:41 - INFO - ##########----------  54% | 5.6s<3.2s | 25.8 it/s
12:03:41 - INFO - ############--------  60% | 6.0s<2.8s | 25.7 it/s
12:03:42 - INFO - ###############-----  75% | 7.1s<1.7s | 25.8 it/s
12:03:43 - INFO - ################----  80% | 7.4s<1.4s | 25.8 it/s
12:03:44 - INFO - ##################--  94% | 8.4s<0.4s | 25.8 it/s
12:03:44 - INFO - #################### 100% | 8.8s<--:-- | 25.8 it/s
12:03:44 - INFO - FINISHED -> TRANSIENT (total steps: 180, successful: 180, runtime: 8785.06 ms)

Python

Part 2: DFN with External Thermal Model

Same feedback topology as notebook 02, but with CellCoSimElectrical instead of CellElectrical. We compare two macro-step sizes to illustrate ZOH approximation error.

Python

Running DFN co-sim with external thermal (dt = 30 s)...
12:03:44 - INFO - LOGGING (log: True)
12:03:44 - INFO - BLOCKS (total: 5, dynamic: 1, static: 4, eventful: 1)
12:03:44 - INFO - GRAPH (nodes: 5, edges: 7, alg. depth: 2, loop depth: 0, runtime: 0.091ms)
12:03:44 - INFO - STARTING -> TRANSIENT (Duration: 1800.00s)
12:03:45 - INFO - --------------------   1% | 0.1s<8.1s | 7.3 it/s
12:03:45 - INFO - ####----------------  20% | 0.3s<0.8s | 57.4 it/s
12:03:45 - INFO - ########------------  40% | 0.5s<0.6s | 59.6 it/s
12:03:45 - INFO - ############--------  61% | 0.8s<0.4s | 59.9 it/s
12:03:45 - INFO - ################----  80% | 0.9s<0.2s | 60.0 it/s
12:03:46 - INFO - #################### 100% | 1.1s<--:-- | 57.8 it/s
12:03:46 - INFO - FINISHED -> TRANSIENT (total steps: 60, successful: 60, runtime: 1140.35 ms)
Running DFN co-sim with external thermal (dt =  5 s)...
12:03:46 - INFO - LOGGING (log: True)
12:03:46 - INFO - BLOCKS (total: 5, dynamic: 1, static: 4, eventful: 1)
12:03:46 - INFO - GRAPH (nodes: 5, edges: 7, alg. depth: 2, loop depth: 0, runtime: 0.092ms)
12:03:46 - INFO - STARTING -> TRANSIENT (Duration: 1800.00s)
12:03:46 - INFO - --------------------   1% | 0.2s<8.6s | 41.5 it/s
12:03:47 - INFO - ###-----------------  17% | 1.2s<4.9s | 59.9 it/s
12:03:47 - INFO - ####----------------  20% | 1.3s<4.8s | 59.6 it/s
12:03:48 - INFO - #######-------------  36% | 2.3s<3.8s | 60.8 it/s
12:03:48 - INFO - ########------------  40% | 2.5s<3.6s | 59.8 it/s
12:03:49 - INFO - ###########---------  56% | 3.5s<2.6s | 59.9 it/s
12:03:50 - INFO - ############--------  60% | 3.8s<2.4s | 58.8 it/s
12:03:51 - INFO - ###############-----  76% | 4.8s<1.4s | 57.5 it/s
12:03:51 - INFO - ################----  80% | 5.0s<1.2s | 59.1 it/s
12:03:52 - INFO - ###################-  96% | 6.0s<0.2s | 58.1 it/s
12:03:52 - INFO - #################### 100% | 6.2s<--:-- | 59.2 it/s
12:03:52 - INFO - FINISHED -> TRANSIENT (total steps: 360, successful: 360, runtime: 6196.86 ms)

Python

Summary

Block	Model	Thermal
`CellElectrothermal`	SPMe / SPM (ODE)	Built-in
`CellCoSimElectrothermal`	Any incl. DFN (DAE)	Built-in
`CellElectrical`	SPMe / SPM (ODE)	External (`LumpedThermal`)
`CellCoSimElectrical`	Any incl. DFN (DAE)	External (`LumpedThermal`)

DFN resolves spatial gradients in both phases but produces a DAE — use the co-simulation blocks.
A smaller macro-step dt reduces ZOH error at the cost of more PyBaMM step() calls.
The external thermal loop extends naturally to multi-cell pack models.