The interfaces between different materials play a key role for the understanding and optimization of batteries. Typical modelling approaches take only the transport across the interface into account and neglect transport along the surface. However, these effects might be highly important for interface phenomena, such as grain boundary transport or surface degradation (e.g. plating). The modelling of this requires the full resolution of the three dimensional electrode structure, since it is not possible to resolve the material interfaces otherwise. In addition, this comes with some numerical challenges, since the computations are expensive and combine effects on different length scales into one simulation. Interface processes have been studied in isolation, but as coupled model it has seen only little attention so far. A first work on this topic can be found in [1]. In this contribution we present our simulation workflow for coupling structure resolved models with surface equations on two dimensional manifolds. Starting from a voxel structure as it is typically obtained from tomography data, we reconstruct an unstructured mesh, with a geometrically well represented surface. On this mesh we can then use a finite volume scheme for the bulk equations, a finite element discretization for the surface models and an adaptive time stepper for the time integration. The resulting implicit systems are solved using Newton’s method. Insights about the robustness and accuracy are given using academic and applied examples. This workflow can support the development of battery models that help to gain a deeper understanding of the interplay between different physical effects and therefore accelerate the improvement of batteries. [1] Sinzig, S., Schmidt, C. P. and Wall, W. A., A Conservative and Efficient Model for Grain Boundaries of Solid Electrolytes in a Continuum Model for Solid-State Batteries, J. Electrochem. Soc. 171, 040505 2024.