Digital simulations on unequally spaced grids.: Part 2. Using the box method by discretisation on a transformed equally spaced grid

The paper demonstrates that using the box method on a transformed equally spaced grid can be accomplished in such a way that the integral flux conservation property of the exact equations will be preserved by the discretised ones. That means, when executing simulations on an exponentially expanding grid, the computed flux becomes virtually independent of grid expansion. Unlike the point or finite element method where the entire concentration profiles must be refined to ensure the accuracy of the simulated flux, the error obtained by the box method can be controlled simply by moving the first concentration point closer and closer to the electrode. This can be done with the smallest possible number of grid points even on strongly expanding grids without affecting the accuracy of the flux computation provided the grid expansion factor ΔY remains ≤0.5. The mathematical explanation of the flux conservation property given here for a simple diffusion problem will be extended in subsequent papers to more relevant systems involving chemical reactions coupled with the charge transfer processes.