Simulation of Electrochemical Problems

Maloy Seton Hall University, South Orange, New Jersey 

Many advances in digital simulation have taken place since the publication of the first edition. Some of these advances have occurred in hardware through the development of the personal computer. Others have taken place by the development of commercial software that will perform specific simulations or will create a computer environment (e.g., a spreadsheet) that will allow one to do simulations without having to write a computer program. Finally, there have been theoretical advances where newer implicit algorithms are used to solve the necessary partial differential equations more efficiently than is possible using the more intuitive explicit methods described herein. 

This revision does not attempt to take many of these recent advances into account, even though some of them are cited in this chapter. Rather, it continues to provide a rigorous foundation for writing programs that will perform explicit finite difference simulations. In learning how to do this, the reader develops an appreciation of the method and, more importantly, its limitations. 

Not the least of these results from the absence of an analytical solution to almost any problem of consequence, except in the limits of the boundary value problem. An appreciation of this limitation and how one may minimize its impact is essential to the utilization of digital simulations in any application. 

Any discussion of the digital simulation of problems involving diffusion begins with a consideration of the combined form of Fick s laws [5], 

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Figure 20.1 Model volume element array used in elementary digital simulations of electrochemical problems. Note that the planar electrode has been placed in the middle of the first volume element in this model.

The equation systems commonly found in the simulation of electrochemical problems have a diagonal structure with a bandwidth 2n+l such that a j = 0 for j > i + n and for i > j n. By particularising the LU decomposition for diagonal systems [extended Thomas algorithm) the above expressions turn into... 

Mocak J, Feldberg SW (1994) The Richtmyer modification of the fully implicit finite difference algorithm for simulations of electrochemical problems. J Electroanal Chem 378 31-37... 

Marques da SUva B, Avaca LA, Gonzalez ER (1989) New explicit finite difference methods in the digital simulation of electrochemical problems. J Electroanal Chem 269 1-14... 

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