THE RICHTMYER MODIFICATION OF THE FULLY IMPLICIT FINITE-DIFFERENCE ALGORITHM FOR SIMULATIONS OF ELECTROCHEMICAL PROBLEMS

The five-level Richtmyer modification of the fully implicit Laasonen f inite difference algorithm is shown to exhibit superb accuracy and rap id convergence for the simulation of electrochemical phenomena, suppor ting the very wide range of values of the dimensionaless diffusion par ameter D (D* = DDELTAt/DELTAx2) from 10 to 10(20). Large values of D* are essential for accurate and efficient simulations of systems invol ving a wide dynamic range of homogeneous kinetic rates. The performanc e is tested by simulations of Cottrellian diffusion and executed using a minor modification of Rudolph's fast implicit finite difference alg orithm. The accuracy of the simulations is verified by comparing simul ated values of time-dependent fluxes and flux integrals and time- and distance-dependent concentrations, with values computed from known ana lytic solutions.