Use of dynamically adaptive grid techniques for the solution of electrochemical kinetic equations: Part 10. Extension of the patch-adaptive strategy to kinetic models involving spatially localised unknowns at the boundaries, multiple space intervals, and non-local boundary conditions, in one-dimensional space geometry

Abstract

The finite-difference patch-adaptive strategy for electrochemical kinetic simulations, described in Part 5 of this series of papers, is extended to time-dependent models in one-dimensional space geometry, involving spatially localised unknowns at the boundaries, multiple space intervals, and non-local boundary conditions. These extensions are of interest, among others, for the modelling studies of: electrochemical adsorption and/or electrocatalytic reactions, liquid ∣ liquid interfaces, amalgam electrodes, electrochemical biosensors, and pattern formation at electrodes. The following new features are included in the strategy. Grid objects, used by the spatial grid adaptation algorithm, are decomposed into interior and boundary subgrid objects, keeping discrete values of the spatially distributed and localised unknowns, respectively. Linear algebraic equation systems, characterised by quasi-block-tridiagonal matrices having variable block dimensions, and isolated block-pentadiagonal rows, are solved by a specially developed variant of the Thomas algorithm, previously published by the present author. Relative error control is applied to localised unknowns. The calculation of consistent boundary solutions takes into account temporal derivatives present in boundary conditions. Accurate a posteriori calculation of temporal derivatives of the localised unknowns is enabled.