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

Strutwolf, Jörg; Britz, Dieter

doi:10.1016/j.jelechem.2003.11.009

Cited by 10 publications

(2 citation statements)

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“…The calculation of the mesh point spacings is performed by an iterative binary search algorithm [31,32]. This algorithm estimates an expansion factor from the smallest space interval, the given number of grid points and the maximal value of the spatial coordinate.…”

Section: Grid Generationmentioning

confidence: 99%

“…During the time stepping process diffusion in each space direction is then treated simultaneously implicit. For the simulation of two dimensional electrochemical diffusion problems this approach has been used employing the CrankNicholson [33], BDF [16,18,32], Rosenbrock [34] and extrapolation [18] (note that extrapolation can also be performed with only one space direction treated implicitly per time sub-step, as has been applied to microband [35], double band [36] and interdigitated array electrode simulation [28]). A disadvantage of taking all space directions implicitly during the time increment is the amount of computer memory and cpu-time necessary for solving the system of (N X þ 1) Â (N Y þ 1) equations during each time step, when the number of grid points in the X and Y direction, N X and N Y becomes high and small time steps are used.…”

Section: The Douglas-gunn Adi Schemementioning

confidence: 99%

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Computational Study of Chronoamperometry at Rectangular Microelectrodes

Strutwolf

2005

Electroanalysis

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Three (space) dimensional diffusion to a rectangular microelectrode of length l and width w, embedded in an infinite coplanar insulator is simulated with boundary conditions for a chronoamperometric experiment. An alternating direction implicit finite difference method (Douglas-Gunn algorithm) utilizing a problem adapted grid is used to solve the diffusion equation. Current transients are computed for different values of the dimensionless length parameter L ¼ l/w, starting with L ¼ 1, i.e., a square electrode. Edge effects at the four sides of the rectangular electrode as well as the vertex effect contribute to the total current. With increasing L the transients approach the behavior of a microband electrode transient, where diffusion is essentially two dimensional. The breakdown of the two dimensional diffusion approach with decreasing values of L is analyzed and quantified. This serves as a guideline for analyzing transients measured with electrodes where the condition l » w is not fulfilled.

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Section: Grid Generationmentioning

confidence: 99%