Use of dynamically adaptive grid techniques for the solution of electrochemical kinetic equations: Part 7. Testing of the finite-difference patch-adaptive strategy on example kinetic models with moving reaction fronts, in one-dimensional space geometry

The patch-adaptive strategy described in Part 5 proves to provide correct, fairly efficient, and nearly automatic solutions to three representative example electrochemical kinetic models in one-dimensional space geometry, that exhibit difficult-to-resolve moving reaction fronts in the electrolyte, away from the electrode. The models describe: double potential step experiments for a simple mechanism of electrochemically generated luminescence, linear potential sweep voltammetry for an EE-DISP mechanism with Nernstian charge transfers and a reversible homogeneous disproportionation reaction, and linear potential sweep voltammetry for an RRC-initiated electropolymerization reaction scheme. The strategy dynamically creates spatio-temporal grids that adaptively concentrate in the regions of the reaction fronts, without any a priori knowledge about their location. Numerical difficulties, such as electric current oscillations observed with the previously described adaptive moving grid technique in the case of moving reaction fronts, do not occur in the present strategy. However, further work is needed to improve the performance of the strategy in the cases of reaction fronts associated with fast and irreversible second-order homogeneous reactions, for which the computational costs are too large. Improvements are also desirable in the case of the simulation of a rapidly moving reaction front occurring in the electropolymerization model, for which the strategy tends to provide incorrect front positions.