In the homogenized model, each voxel consists of a mixture of active material and electrolyte. Therefore, the system of partial differential equations solved by the BESTmeso solver does not consist of separate equations for active material, the electrolyte and the interface between them as in the fully resolved model.

The homogenized model uses a volume averaged 1D version of the microscopic model outlined in Latz et al., 2013. This is basically identical to the DFN-model.

The equations of the fully resolved model for diffusion and migration as well as for charge conservation and electroneutrality of the electrolyte (equations (121) and (119) ) and Ohm’s law for the active materials (equation (117) ) are therefore supplemented by additional source terms. These source terms account for the Butler-Volmer current from electrolyte to active material and vice versa through the (no longer resolved) interface between these materials. The 1D movement of Lithium ions and electrons is described by the following three equations:  

The equation of diffusion in the active materials transforms to a radial diffusion on the representative active particle scale:

and

with the flux

Finally, the Butler-Volmer interface condition depends now on the overpotential at the boundary of the spherical particles.

In the fully resolved model, the interface is located between active material and electrolyte voxels. In contrast to this, the interface in the homogenized model is within the 1D voxels and not resolved in the structure.

Parameters, appearing in the equations above are:

The computation of effective properties in the homogenized model precedes charging or discharging simulations, which are run with BESTmeso solver. For a full battery simulation, effective parameters for each electrode are calculated separately.

The computed effective properties can be found in the Result Map of charging or discharging simulation under FoundMesoParameters and are displayed in the Results Report. In the case of an electrode simulation, calculated effective parameters are always listed under Cathode.

The following effective properties are computed:

For electrolyte:

• - effective ionic diffusivity
• - effective ionic conductivity

Both properties are computed for the x-direction of the electrode, using algorithms of ConductoDict with EJ solver, assuming symmetric boundary conditions of the structure and taking into account the (non-zero) electrolyte diffusivity and conductivity respectively. The diffusivity or conductivity constants for all active materials are set to zero. In case of porous binder, effective ionic diffusivity and conductivity are used, for non-porous binder both constants are also set to zero.

For active materials and binder:

• - effective electronic conductivity

The parameter is computed using the same setting as for electrolyte (ConductoDict algorithms with EJ solver, computation in X-direction of the electrode, symmetric boundary conditions). In this case, the conductivity of electrolyte is set to zero, while for all active materials and binder their electronic conductivity is considered.

For active materials:

• - effective radius of representative spherical particle of active material p
•  - specific surface area between electrolyte and active material p

The computation of effective radius is similar to the algorithm Estimate Grain Diameters in the GrainFind module. The effective radius for each active material is found as the average radius of all particles of this active material. All particles are considered as spheres in this estimation.

The specific surface area is calculated as voxelized area between electrolyte and connected voxels for each active material. The voxel connectivity is checked according to the algorithm, which is explained in Analyze Battery for the structure with symmetric tangential boundary conditions.

With GeoDict 2025 SP3, the volume fraction of unconnected material is also considered when computing the transferred charges and the SOC in order that it matches to the fully resolved model. The electrochemical cell behavior, i.e. the shape of the charging curve, is not affected.

For separator:

In case of porous separator, the effective values for ionic conductivity and ionic diffusivity and the porosity are used in the same way as for fully resolved simulations.