Use of dynamically adaptive grid techniques for the solution of electrochemical kinetic equations: Part 6. Testing of the finite-difference patch-adaptive strategy on example models with solution difficulties ... więcej

Use of dynamically adaptive grid techniques for the solution of electrochemical kinetic equations: Part 6. Testing of the finite-difference patch-adaptive strategy on example models with solution difficulties at the electrodes, in one-dimensional space geometry / L. K. Bieniasz // Journal of Electroanalytical Chemistry [Dokument elektroniczny]. – 2000, Vol. 481, Iss. 2, s. 134-151 : tab., wykr. – Tryb dostępu: https://www.sciencedirect.com/science/article/pii/S0022072899004593. – Bibliogr. 44 poz., Abstr. – doi: 10.1016/S0022-0728(99)00459-3. – ISSN 0022-0728

The patch-adaptive strategy described in Part 5 proves to provide correct, fairly efficient, and nearly automatic solutions to six representative example electrochemical kinetic models in one-dimensional ... więcej

The patch-adaptive strategy described in Part 5 proves to provide correct, fairly efficient, and nearly automatic solutions to six representative example electrochemical kinetic models in one-dimensional space geometry, that exhibit difficult-to-resolve local spatial and temporal solution structures at the electrodes. The models describe: the square-wave controlled potential transient for an uncomplicated heterogeneous charge transfer reaction, the potential step method and linear potential sweep voltammetry for the standard catalytic reaction mechanism with a pseudo-first-order homogeneous reaction, linear potential sweep voltammetry for an EC reaction mechanism involving a follow-up homogeneous dimerisation, steady-state voltammetry at a rotating disc electrode, and steady-state voltammetry at a spherical microelectrode. These examples are characterised by extremely thin reaction layers and other instances of local spatial regions of considerable variations of the solution, including transient effects caused by temporal discontinuities of boundary conditions. The strategy creates dynamically spatio-temporal grids well adapted to such solution structures, without any a priori knowledge about their location. The accuracy of the numerical solutions proves well controlled by means of error tolerance parameters. Numerical difficulties observed with the previously described adaptive moving grid technique do not occur in the present strategy. However, further work is needed to improve the performance of the strategy in the cases of thin reaction layers associated with fast second-order homogeneous reactions, and boundary layers associated with hydrodynamic electroanalytical methods, for which the computational effort appears too large.