Comparison of flux approximations in electrochemical digital simulation

Both on an exponentially expanding grid in X-space, and the corresponding equidistant grid in transformed Y-space, fluxes were expressed as either gradient approximations using a variable number of points, or as the integral of rates of changes of the concentrations with time over the whole diffusion space. The two cases chronoamperometric and chronopotentiometric boundary conditions were simulated. Results show that in X-space, the gradient approximation produces smaller errors, even using the two-point gradient formula, and the integration method produced larger errors. In Y-space, however, when using an improved discretisation formula by Bieniasz, the situation is reversed, the gradient approximations leading to higher errors than the integral method. What is more, there is a very convenient reduced formula due to Rudolph with errors comparable to those from the full integration approximation.