Thin layer flow cells are used in electrochemical research as experimental devices which allow to perform investigations of electrocatalytic surface reactions under controlled conditions using reasonably small electrolyte volumes. The paper introduces a general approach to simulate the complete cell using accurate numerical simulation of the coupled flow, transport and reaction processes in a flow cell. The approach is based on a mass conservative coupling of a divergence-free finite element method for fluid flow and a stable finite volume method for mass transport. It allows to perform stable and efficient forward simulations that comply with important physical constraints, namely mass conservation and maximum principles for the involved species. In this context, several recent approaches to obtain divergence-free velocity approximations from finite element simulations are discussed. In order to perform parameter identification, the forward simulation method is coupled to standard optimization tools. After an assessment of the inverse modeling approach using hypothetical, but realistic data, first results of the identification of solubility and transport data for O2 dissolved in organic electrolytes are presented. A plausibility study for a more complex situation with surface reactions concludes the paper and shows possible extensions of the presented numerical tools. (C) 2016 Elsevier Ltd. All rights reserved.