Solving Electrochemical Models
Due to the highly nonlinear nature of electrode kinetics, some electrochemical models can be difficult to solve. This section includes some general tips and tricks to facilitate model solving, trouble shooting, and to improve solution accuracy.
General Current Distribution Problems
Start with the following suggestions if you encounter difficulty solving a problem.
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Make sure that the potential levels are “boot-strapped” somewhere in the model, preferably by grounding one electrode. If there is no potential level defined anywhere in the model, your model may have infinitely many solutions, and the model will not converge.
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Consider using a Stationary with Initialization or a Time Dependent with Initialization study. Both these studies will use a Current Distribution Initialization study step as a first step to solve for the potentials only. If you run into problems solving for the second step in this study you may have to change the “Current distribution type” setting to Secondary on the Current Distribution Initialization study step node, and also review the Initial Values as described in the next bullet.
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Review the Initial Values, especially the potentials. Suitable initial potential values can usually be derived making a “potential walk” through the geometry, starting at the grounded boundary. Compute electric and electrolyte potentials in other domains by assuming equilibrium potential differences between electrode and electrolyte for the main electrode reactions.
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Switch to Linearized Butler-Volmer kinetics (or a Primary current distribution) while troubleshooting. This can be useful to help achieve a solution for a model that does not solve with nonlinear kinetics, thereby indicating suitable initial values for the nonlinear problem.
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If your model contains porous electrodes, try refining the mesh resolution in these domains, especially toward the electrolyte boundaries.
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Electrochemistry Interfaces
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Specifying Initial Values and Meshing Techniques in the COMSOL Multiphysics Reference Manual
Electrochemistry Coupled to Mass Transport
If the model involves electrochemistry coupled to mass transport, here are a few things to try to help improve model convergence.
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Review the Initial Values for the concentration values. Zero initial concentration values can be unsuitable for tertiary current distribution problems and battery simulations, since they could imply that no charge carriers or no reacting material is present.
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If steep concentration gradients are expected close to electrode surfaces, use boundary layer meshing or finer mesh Size settings at these boundaries.
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When setting up user-defined kinetics expressions, avoid evaluating negative concentrations by using expressions such as max(c, eps^2), where eps is the machine epsilon (a very small but finite number).
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Try to solve for low currents and low overpotentials first, then increase the cell load (for stationary problems this can be done using an auxiliary sweep with continuation).
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If a problem involving mass transport is hard to solve for high currents, but solves for low currents, it might be due to mass transport limitations. In this case, review the transport parameter values and check that the current magnitudes are reasonable. If the current densities are unreasonably high, review the electrode reaction settings.
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For time-dependent problems that run into convergence problems after a certain time, review the solution at the last time-step. If the solution of a reactant reaches zero or a maximum value (for insertion electrodes in batteries) when the convergence issues occur, the current load of the model is too high in relation to your initial concentrations or mass transport properties.
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Electrochemistry Interfaces
In the COMSOL Multiphysics Reference Manual:
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2D and 3D Boundary Layer Meshes
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Stationary and Parametric Sweep
Setting up a Study Sequence for Multiphysics Problems
For multiphysics problems, try to adjust the study sequence.
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Solve certain physics interfaces in a sequence. This can in many cases reduce computational time and improve convergence. Analyzing the results when solving a physics interface separately can also help when troubleshooting a nonconverging model.
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A good strategy is often to solve for the potentials only (that is, disable mass transport and flow interfaces), using a stationary study step, before solving the full model in the study sequence. In this way the stationary solution is used as initial values for the following steps. This can be manually by modifying the settings of the study node, or in an automated way by using the Stationary with Initialization or Time Dependent with Initialization study sequences, as described above.
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In many models the flow profile is only slightly (or not at all) affected by changes in current density. Therefore it can be a good strategy to solve separately for the flow early in the study sequence, and then solve for the other physics interfaces in the subsequent steps. (If the flow is not affected at all by the current distribution, solving for the flow can be disabled entirely in consecutive steps.)
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Electrochemistry Interfaces
In the COMSOL Multiphysics Reference Manual:
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Studies and Solvers
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Analyzing Model Convergence and Accuracy
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Achieving Convergence When Solving Nonlinear Equations
Time-dependent Problems with Load Steps
For time-dependent problems, try the following to address accuracy and convergence issues with regards to sudden current or potential load steps.
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Use smoothed current or potential load functions in order to avoid instantaneous or discrete load steps.
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Add a double layer capacitance to the model, which can improve the numerical stability.
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Reduce the Maximum step taken by the solver if you want to prevent the solver from “missing” short square load steps, or change the Steps taken by solver setting from Free to Strict, or Intermediate, to control the time steps using the Times text field. Using the Events interface can also be an option in certain cases if the load cycle itself varies dynamically.
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Double Layer Capacitance
In the COMSOL Multiphysics Reference Manual:
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Step and Time Dependent
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Building a COMSOL Multiphysics Model and The Events Interface
Solver Settings
Try adjusting the solver settings.
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In rare cases, try to increase the Maximum number of iterations.
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If you know the order of magnitude of the dependent variables beforehand, setting the scaling method to Manual for these can improve convergence and the accuracy of the results. This may be of special importance when solving for concentrations that are initially very small but where the final order of magnitude is know a priori. This could be the case for the active species in a battery model, for example.
In the COMSOL Multiphysics Reference Manual:
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Studies and Solvers
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Analyzing Model Convergence and Accuracy
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Achieving Convergence When Solving Nonlinear Equations
 
Electrochemistry Studies and Study Steps and Cyclic Voltammetry in the COMSOL Multiphysics Reference Manual
In multicomponent systems it is rarely straightforward to predict the rest potential and direction of current flow. The Current Initialization step in COMSOL Multiphysics does this for you but is only correct if concentrations and formal potentials for all electrode reactions are specified precisely and with respect to a common reference scale.
Electrochemistry Studies and Study Steps in the COMSOL Multiphysics Reference Manual
Studies and Solvers and Building a COMSOL Multiphysics Model in the COMSOL Multiphysics Reference Manual