Digital Simulation of Two-Dimensional Mass Transfer Problems in Electrochemistry Using the Extrapolation Method

Abstract

In this article we report the application of the extrapolation method to electrochemical problems involving two-dimensional mass transfer. The extrapolation method is based on a combination of fully implicit difference schemes and was previously successfully used in solving electrochemical processes including linear diffusion. The diffusion equation to a microband electrode under diffusion controlled conditions is solved by the extrapolation method and the alternating implicit direction technique. The results are compared. Both ®nite difference methods have the same order of accuracy but the extrapolation technique has a higher order of stability making it preferable for stiff relaxation problems and for an accurate simulation of short time behavior.

Several ways to simulate time dependent liquid junction potentials by finite differences

“…In the case of expanding time intervals (see later), this was not convenient, as unequal time intervals reduce the order of three-point BDF to O(ıT), so four-point BDF would be needed to achieve the same order [38]. It was more convenient in this case to use backward implicit with extrapolation [39][40][41][42], which is also O(ıT 2 ) (for the simple second-order extrapolation method). The method requires three operations per time step rather than one, but as comparatively very few time steps were needed if they were expanding with time, computation was extremely fast, as will be seen.…”

Higher-order spatial discretisations in electrochemical digital simulation. Part 5: application to stationary ultramicrodisc electrode simulation

“…In this situation it is known that conformal transformation is less efficient [9,30,36]. In conformal oblate spheroidal coordinates the equiconcentration lines are then not parallel to the H-axis, as depicted in Fig.…”

“…This can lead to oscillating solutions, often noted with potential step transient simulations [7][8][9][10]. A better stability (L 0 -stable, for the definitions of A 0 and L 0 -stability see [11], in connection with electrochemical simulation see [12]) has been achieved in two dimensional electrochemical simulation by using extrapolation [9,13] and by the strongly implicit method [14]. The backward differentiation formula (BDF) [8,15], although not being L 0 -stable [16], is nevertheless a good choice, not responding with oscillations for k values up to about 5 (see below).…”